Match ends, Bournemouth 0, Everton 2.
Everton reached the FA Cup quarter-finals for the fourth time in five seasons as strikes by Ross Barkley and Romelu Lukaku saw off Bournemouth.
It could have turned out differently for the Cherries had Charlie Daniels converted his first-half penalty, which was superbly saved by Joel Robles.
Barkley gave the Toffees the lead when his 20-yard strike looped in off the boot of Dan Gosling in the 55th minute.
Lukaku settled the tie when he slammed in from close range.
Bournemouth went close through Gosling, whose header from four yards was straight at Robles, and Junior Stanislas' deflected free-kick narrowly beat the Everton upright.
Martinez shows the way with strong selection
See what happens when you play your best side?
It is now expected for managers to rest their best players for domestic cups - Bournemouth made six changes today, Arsenal made nine and Hull made 10.
So when Everton boss Roberto Martinez fielded an unchanged line-up from the one that started in their last league outing, it would have heartened fans of the competition and those who travelled down from Merseyside.
Bar a small spell in the second half when Bournemouth threatened, Everton were dominant.
Second-half tweaks reap rewards for Everton
Everton found it difficult to convert that dominance into chances in the first half, with striker Lukaku pulling out wide instead of playing as the target man and Barkley playing deeper.
The system was tweaked by the Spanish boss after the break. Within seconds of the restart the ball was pinged to Lukaku, who chested it into the path of Aaron Lennon.
The breakthrough came 10 minutes in, when Barkley was fed a pass near the edge of the area before striking the ball which took a huge deflection off Gosling and deceived Adam Federici. Watching England manager Roy Hodgson would have been impressed by his new midfield maestro.
Lukaku then showed his predatory skills inside the area when he lashed in after team-mate Gareth Barry had flicked on an Everton corner.
Bournemouth pay for miss
League survival is paramount, of course, but a good cup run could have been what the doctor ordered for Eddie Howe's side.
It looked as if it might be Bournemouth's day when they were awarded a penalty after James McCarthy had inexplicably handballed in the area.
Daniels took possession of the ball and launched a fierce, but easily readable, effort which Robles saved. Three Cherries players then all went for the loose ball, which resulted in Juan Iturbe firing wide.
Gosling should have done better with his second-half header, and Stanislas was unlucky. But truth be told Bournemouth did not deserve anything from the tie.
Bournemouth boss Eddie Howe, speaking to BBC Sport:
"Everton had the extra quality and in key moments in the game we did not take our chances.
"It looked like we were going to score the rebound from the penalty save but that is one of those things, players eager to get on the end of it. No blame on Charlie, though.
"We were well in the game at half-time. It was a real 50-50 but the deflected goal was key.
"I have been on record many times saying the league is our priority."
Everton boss Roberto Martinez:
"We will take it step by step. It was important that we showed we can adapt to this game, now we want to get a really good period in the league.
"The only thing that has been missing has been wins at home and we are looking to change that.
"The League Cup semi-final gave us an inspiration to want to be at Wembley every chance we can. Clearly the group is hungry for that kind of occasion."
The stats you need to know
- Barkley has been involved in 20 goals in all comps this season, more than any other English PL midfielder (12 goals and eight assists).
- Lukaku has scored in each of his four FA Cup appearances for Everton and in both games v Bournemouth this season.
- Bournemouth have lost four of their last five home games.
- The Toffees have only failed to score in one of their last 14 games on the road in all competitions.
- Bournemouth have not beaten a top division side in the FA Cup since 1984 and overall have won just three of 33 matches against clubs from the top flight (W3 D7 L23).
Bournemouth travel to Watford next Saturday, and Everton are at struggling Aston Villa on Tuesday, 1 March.
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- 12IturbeBooked at 66minsSubstituted forMurrayat 71'minutes
- 4GoslingBooked at 45minsSubstituted forA Smithat 77'minutes
- 16MacDonaldSubstituted forRitchieat 63'minutes
- 17KingBooked at 68mins
- 15A Smith
- 25Funes Mori
- 16McCarthyBooked at 18mins
- 20BarkleySubstituted forMirallasat 81'minutes
- 10LukakuSubstituted forNiasseat 81'minutes
- Martin Atkinson
- Shots on Target
Second Half ends, Bournemouth 0, Everton 2.
Kevin Mirallas (Everton) wins a free kick on the right wing.
Foul by Charlie Daniels (Bournemouth).
Attempt missed. Aaron Lennon (Everton) right footed shot from the right side of the box is too high. Assisted by Seamus Coleman with a headed pass.
Attempt missed. Joshua King (Bournemouth) header from very close range is too high. Assisted by Junior Stanislas with a cross following a set piece situation.
Matt Ritchie (Bournemouth) wins a free kick on the right wing.
Foul by Gareth Barry (Everton).
Attempt missed. Kevin Mirallas (Everton) right footed shot from outside the box is high and wide to the right. Assisted by Tom Cleverley.
Attempt missed. Matt Ritchie (Bournemouth) left footed shot from outside the box is high and wide to the left.
Simon Francis (Bournemouth) wins a free kick in the defensive half.
Foul by Oumar Niasse (Everton).
Substitution, Everton. Oumar Niasse replaces Romelu Lukaku.
Substitution, Everton. Kevin Mirallas replaces Ross Barkley.
Attempt blocked. Joshua King (Bournemouth) right footed shot from the left side of the box is blocked. Assisted by Junior Stanislas.
Attempt blocked. Ross Barkley (Everton) right footed shot from the centre of the box is blocked. Assisted by Romelu Lukaku.
Substitution, Bournemouth. Adam Smith replaces Dan Gosling.
Goal! Bournemouth 0, Everton 2. Romelu Lukaku (Everton) right footed shot from very close range to the centre of the goal. Assisted by Gareth Barry following a corner.
Corner, Everton. Conceded by Eunan O'Kane.
Attempt blocked. Ross Barkley (Everton) right footed shot from the centre of the box is blocked. Assisted by Aaron Lennon.