Match ends, Brighton and Hove Albion 0, Chelsea 4.
Chelsea boss Antonio Conte complained about the "negative press" surrounding his side as he praised his players for their win over a spirited Brighton.
The Premier League champions moved up to third as two goals in the opening six minutes put them on the way to victory.
Eden Hazard opened the scoring for the visitors with a neat finish from inside the box and midfielder Willian added a second from 18 yards, after a slick move that he started, to leave Chris Hughton's side facing an uphill task.
The hosts' response was impressive. They should have had a penalty when Chelsea stand-in goalkeeper Willy Caballero upended defender Ezequiel Schelotto, while Israeli striker Tomer Hemed was brilliantly denied by the former Manchester City shot-stopper.
Netherlands midfielder Davy Propper headed against the post and Schelotto went close after the break as Brighton pushed to get back in the game.
Chelsea were always a threat, though, and Willian had a free-kick pushed on to the post by Brighton keeper Mat Ryan before Hazard scored his second with a fine solo effort and Victor Moses' late goal completed the victory.
"We are unbeaten in 12 games," said Conte. "A lot of the time the press tries to see the negative aspect, and not the positive aspect. This team, with many problems, is unbeaten in 12 games in all competitions.
"To win in this way, despite not having five important players, means every player deserves to have a chance and every player has to fight to play.
"Now we have to continue in this way. Every player showed great responsibility, and felt the responsibility. To grow in this aspect is very important for us."
Conte could savour a first league triumph of 2018 for his side and a strong finish to the game, although he lost defender Andreas Christensen to a head injury in the second half and was already without captain Gary Cahill, keeper Thibaut Courtois and Cesc Fabregas.
Hughton's concerns continue, despite his team's battling qualities. This defeat means they have won only one of their past 13 league games.
Fresh approach unrewarded for Brighton
Hughton tried something different at the back, selecting five defenders to try to halt his side's costly tendency to concede from set-pieces.
But it was in open play where they simply could not live with a team they have not beaten since 1933.
Brighton, with a steady central-defensive pairing of Lewis Dunk and Shane Duffy, have had a relatively mean defence this term - only the league's top eight sides had conceded fewer than them before this defeat.
Yet a mixture of misfortune and sloppy play cost them, with Hazard the benefactor on both occasions.
First, Moses' early cross was deflected by Dale Stephens into the path of the Belgian, who quickly found a gap to score the opener. Then Duffy lost possession, allowing Hazard to zip forward and stroke home the third.
There were positives for the Seagulls. They caused Chelsea problems and, had the video assistant referee been in use, they could well have been awarded a penalty when Schelotto was felled.
The industrious Argentina full-back combined well with Pascal Gross down the right flank and will soon have a £14m centre-forward to aim for in the shape of new signing Jurgen Locadia.
Who needs a target man when you've got these two?
Like their opponents, goals had been hard to come by for Chelsea recently, with only three in their past five games in all competitions - including three consecutive goalless draws.
This was some way to end the drought.
With striker Alvaro Morata, who had been struggling to score, suspended, Conte turned to Michy Batshuayi, who was hoping for an upturn in form after not scoring in the league since netting two against Watford in October.
Conte has reportedly spent much of the January transfer window so far searching for a target man who would make Batshuayi's first-team prospects even bleaker, after only four starts this term. Big centre-forwards such as Peter Crouch, Andy Carroll and Christian Benteke have all been linked with a move to Stamford Bridge.
That search might go on because Batshuayi, despite combining well with Hazard for Willian to score the second, failed to score.
But with that duo in this type of blistering form, Chelsea can ravage teams even without a free-scoring striker.
Former Everton midfielder Ross Barkley, signed to add attacking threat in the final third, was on the bench and not used at the Amex Stadium.
Conte opted to bring on 21-year-old Belgian Charly Musonda instead, and his deft lob created the fourth goal for Moses.
Man of the match - Willian (Chelsea)
'I saw important things' - what they said
Brighton manager Chris Hughton, speaking to BBC Sport: "It was a very difficult afternoon for us. The biggest disappointment is that 4-0 was not a true reflection of the game. We did come on to a bit of a game after going 2-0 down and we had decent opportunities, but we are finding it difficult to find the goals we need.
"I thought there were two [penalties that could have been given]. We see them briefly afterwards, but when you are Brighton playing at home to Chelsea you need as many things to go for you as possible.
"The second I didn't see well but the first one I thought it was a penalty. I thought we responded well but then we conceded two poor goals - and that made the scoreline not a reflection of the game."
Chelsea manager Antonio Conte, speaking to BBC Sport: "It was an important performance. We started very well and scored quickly, with good combinations. We started with a lot of worries, for injuries and suspensions, but the response of the team was incredible. I am very happy for this. Another clean sheet.
"Today it was a really good performance of the team. We moved the ball quickly, we tried to find the players between the lines, to have good combinations. I saw important things. Now we have to continue."
Hazard closes on Chelsea greats - the stats
- Hazard has now scored (65) or assisted (37) in 102 Premier League goals for Chelsea; taking him ahead of Gianfranco Zola (101) to outright third for the club in the competition (Frank Lampard 237, Didiero Drogba 159).
- Brighton have picked up just one win from their past 13 Premier League games (D5 L7), failing to score in nine of these.
- Chelsea have won 45 of their 76 away games against newly promoted sides in the Premier League, a joint-high figure (Arsenal have also won 45).
- The Blues extended their top-flight unbeaten run to eight games (W5 D3), their longest streak without a defeat since March (also eight).
- Willian made his 50th consecutive Premier League appearance, the longest current run of any player in the competition.
- Hazard's opener was his 100th goal in league football (now 101), with 65 coming for Chelsea and 36 for Lille.
- Willian has been directly involved in eight goals in his last five Premier League starts for Chelsea (3 goals, 5 assists), as many as he managed in his previous 20.
- Batshuayi registered his first assist in his last 31 Premier League appearances, since he set up Diego Costa on his debut in the competition in August 2016.
Brighton travel to Middlesbrough in the fourth round of the FA Cup on Saturday, 27 January (15:00 GMT), while Chelsea head to the Emirates on Wednesday to face Arsenal in the second leg of their Carabao Cup semi-final (20:00 GMT)
- 21SchelottoBooked at 36mins
- 18GoldsonBooked at 79mins
- 22DuffyBooked at 56mins
- 13GroßSubstituted forKayalat 68'minutes
- 10HemedSubstituted forMurrayat 68'minutes
- 20MarchSubstituted forIzquierdoat 83'minutes
- 27ChristensenSubstituted forDavid Luizat 58'minutes
- 3AlonsoSubstituted forZappacostaat 75'minutes
- 22WillianSubstituted forMusondaat 81'minutes
- 10E Hazard
- 30David Luiz
- 37dos Reis Carvalho
- Jonathan Moss
- Shots on Target
Second Half ends, Brighton and Hove Albion 0, Chelsea 4.
Foul by N'Golo Kanté (Chelsea).
Glenn Murray (Brighton and Hove Albion) wins a free kick in the defensive half.
Attempt blocked. José Izquierdo (Brighton and Hove Albion) right footed shot from the centre of the box is blocked. Assisted by Dale Stephens.
Attempt missed. Glenn Murray (Brighton and Hove Albion) header from the centre of the box is too high. Assisted by Beram Kayal with a cross.
Goal! Brighton and Hove Albion 0, Chelsea 4. Victor Moses (Chelsea) left footed shot from the centre of the box to the bottom right corner. Assisted by Charly Musonda with a through ball.
Charly Musonda (Chelsea) wins a free kick on the right wing.
Foul by Davy Pröpper (Brighton and Hove Albion).
Attempt saved. Michy Batshuayi (Chelsea) left footed shot from outside the box is saved in the centre of the goal. Assisted by Eden Hazard.
Substitution, Brighton and Hove Albion. José Izquierdo replaces Solly March.
Substitution, Chelsea. Charly Musonda replaces Willian.
Attempt blocked. David Luiz (Chelsea) right footed shot from outside the box is blocked.
Connor Goldson (Brighton and Hove Albion) is shown the yellow card for a bad foul.
Eden Hazard (Chelsea) wins a free kick in the attacking half.
Foul by Connor Goldson (Brighton and Hove Albion).
Goal! Brighton and Hove Albion 0, Chelsea 3. Eden Hazard (Chelsea) right footed shot from the centre of the box to the bottom left corner. Assisted by Willian.
Substitution, Chelsea. Davide Zappacosta replaces Marcos Alonso.
Michy Batshuayi (Chelsea) wins a free kick in the attacking half.
Foul by Dale Stephens (Brighton and Hove Albion).