Match ends, Everton 3, Middlesbrough 1.
Everton extended their winning run to four games in the Premier League with a victory over Middlesbrough that sent them second in the table.
A Maarten Stekelenburg own goal, under pressure from Alvaro Negredo, put the visitors ahead at Goodison Park.
But Gareth Barry levelled on his 600th top-flight appearance following a Kevin Mirallas corner three minutes later.
Seamus Coleman's smart finish and a deft Romelu Lukaku touch then wrapped up the points for Everton by half-time.
Both sides threatened little after the break, with Middlesbrough unable to trouble the Toffees and the hosts happy to maintain their unbeaten start.
That record means boss Ronald Koeman, whose side drew on the first day with Tottenham, has enjoyed the best opening five-game spell of any Everton manager in the Premier League.
Barry hits the 600-mark
Barry has crept quietly towards 600 Premier League appearances - joining Frank Lampard (609) and Ryan Giggs (632) - but the former England international's role has never been undervalued and the 35-year-old is now enjoying some of the best form of his career under new boss Koeman.
Since making his debut for Aston Villa at the end of the 1997-98 campaign, the versatile midfielder has played at least 30 top-flight games in all but one season and again proved pivotal at Goodison Park.
Goals are rarely part of the package, however, but Barry showed plenty of composure to slot home his second of the season after Mirallas' corner had pin-balled around the Boro box.
At the other end, Barry complemented new signing Idrissa Gueye perfectly in Everton's deep-lying midfield pair.
Barry, booked for an altercation with Gaston Ramirez, broke up several Middlesbrough attacks with Gueye's boundless energy mopping up anything his veteran team-mate might have missed.
He was withdrawn by Koeman with two minutes to go, the home crowd showing their appreciation for the Premier League stalwart.
Boro's second-half troubles continue
Middlesbrough's successful promotion bid last season was built on having the Championship's meanest defence, but they had no answer to a rampant Everton on Saturday.
Individual mistakes cost Aitor Karanka's side last week in a defeat by Crystal Palace, and they were sliced open on several occasions on the way to a second successive loss.
It had started so well for the visitors when Negredo rose highest from a deep George Friend delivery to challenge Stekelenburg - watching the keeper drop the ball into his own net.
It may well have been ruled a foul, with the Spaniard appearing to head the goalkeeper's gloves.
Former Manchester City striker Negredo was Karanka's headline-grabbing summer acquisition, but after that contribution to the opener he was unable to trouble the home back four.
Negredo had little to work with as a lone striker, and despite his best attempts to hold up play, the Valencia loanee was unable to link up with playmaker Ramirez.
Uruguayan Ramirez, out of favour when Koeman was in charge of Southampton, was replaced by summer signing Viktor Fischer as Karanka looked to add spark to his attack, but to no avail.
It means Karanka's side are still yet to score in the second half of a Premier League match this season.
Everton's attacking wealth
Koeman has a wealth of attacking talent at his disposal and the Dutchman showed last week, when he removed Ross Barkley at half-time against Sunderland, that he is willing to chop and change to get the best from those resources.
Barkley, also hoping to force his way back into new England boss Sam Allardyce's squad, looked determined to prove his worth to Koeman at Goodison Park and his quick feet and change of pace caused problems for the visitors' defence.
Koeman seems to be now getting the best from £25m man Bolasie, too, and it was the winger whose teasing, in-swinging cross from the right needed only the slightest of touches from Lukaku to take it past Valdes.
Bolasie's tricks may make his showreel great viewing, but with the likes of Barkley, Mirallas, Gerard Deulofeu and Aaron Lennon for competition he knows he must prove effective in the final third.
Before his assist for Lukaku, the pair combined to release full-back Coleman, who weaved his way off the right flank and across the Middlesbrough penalty area before wrong-footing Valdes with a low, left-footed shot.
Dutchman Koeman will be delighted with his side's attacking performance, but there was cause for concern as Belgium international Lukaku was forced off in the second half with an injury.
Man of the match - Ross Barkley
What they said
Everton manager Ronald Koeman: "It's a good start in terms of points but the most important thing is the way we get the points.
"You see the reaction of the fans - they like it. The team is more aggressive but they need to run more and press more."
Middlesbrough manager Aitor Karanka: "Everton had to play their best to beat us. We started really well but we were a little bit lost in the last 10-15 minutes of the first half.
"I can be happy with the attitude of the team because other teams would have lost five, six or 7-1. We were battling to the end."
The stats you need to know
- Everton have won four of their first five league games for the first time since 1978-79, when they finished fourth in the First Division.
- Middlesbrough failed to direct a single shot on target in the game but still scored - only the 10th time that has happened in the Premier League since the statistic began being recorded in 2003-04.
- Gareth Barry has scored two goals in his last four Premier League games, as many as in his 95 before that.
- Romelu Lukaku has now scored against 21 different teams in the Premier League.
- Lukaku has netted four goals in his last two games for Everton in all competitions after failing to find the back of the net in the previous 13.
Everton host Norwich in the EFL Cup on Tuesday and will then hope to extend their unbeaten run in the Premier League when they visit Bournemouth next Saturday.
Middlesbrough entertain Tottenham at the Riverside on Saturday before Aitor Karanka's outfit travel to the London Stadium for the first time to face West Ham.
- 22StekelenburgBooked at 22mins
- 18BarryBooked at 45minsSubstituted forCleverleyat 90+1'minutes
- 11MirallasSubstituted forDeulofeuat 72'minutes
- 10LukakuSubstituted forE Valenciaat 66'minutes
- 19E Valencia
- 25Funes Mori
- 4AyalaBooked at 37mins
- 14de Roon
- 34ForshawSubstituted forClaytonat 84'minutes
- 24NsueSubstituted forNugentat 59'minutes
- 21RamírezSubstituted forFischerat 70'minutes
- Lee Mason
- Shots on Target
Second Half ends, Everton 3, Middlesbrough 1.
Foul by Gerard Deulofeu (Everton).
George Friend (Middlesbrough) wins a free kick in the defensive half.
Substitution, Everton. Tom Cleverley replaces Gareth Barry.
Enner Valencia (Everton) wins a free kick on the left wing.
Foul by Antonio Barragán (Middlesbrough).
Ross Barkley (Everton) wins a free kick in the attacking half.
Foul by Daniel Ayala (Middlesbrough).
Ross Barkley (Everton) wins a free kick in the attacking half.
Foul by Marten de Roon (Middlesbrough).
Foul by Adam Clayton (Middlesbrough).
Leighton Baines (Everton) wins a free kick in the defensive half.
Substitution, Middlesbrough. Adam Clayton replaces Adam Forshaw.
Offside, Middlesbrough. Marten de Roon tries a through ball, but Viktor Fischer is caught offside.
Offside, Everton. Maarten Stekelenburg tries a through ball, but Enner Valencia is caught offside.
Attempt blocked. Viktor Fischer (Middlesbrough) right footed shot from outside the box is blocked. Assisted by Marten de Roon.
Attempt blocked. Stewart Downing (Middlesbrough) left footed shot from outside the box is blocked.
Offside, Middlesbrough. Marten de Roon tries a through ball, but Álvaro Negredo is caught offside.
Substitution, Everton. Gerard Deulofeu replaces Kevin Mirallas.