Everton reached the Emirates FA Cup sixth round for the fourth time in five seasons with second-half goals from Ross Barkley and Romelu Lukaku enough to beat Bournemouth.
The Cherries, in the fifth round for the first time in 27 years and only the fourth time in their history, had a golden opportunity to take the lead with a Charlie Daniels penalty shortly before half-time.
Bournemouth 0-2 Everton
Emirates FA Cup
Saturday 20 February 2016
Winning sides receive £180,000 from prize fund
Click here for Opta match page
But the former Tottenham left-back saw his spot kick beaten away by Joel Robles – an FA Cup winner with Wigan in 2013 – and England midfielder Barkley made him pay with a finish of real quality from the edge of the box on 55 minutes.
And Lukaku made certain with his 21st goal of a stellar season.
The Toffees started the game with purpose and when Barkley burst into the box on four minutes he perhaps should have done more to test Adam Federici.
Juan Iturbe, signed on loan from Roma last month, had the Bournemouth fans on their feet with a driving run through the heart of the Everton defence, but he fluffed his lines with a weak finish.
Former Everton midfielder Dan Gosling then blocked a shot from James McCarthy and defender Ramiro Funes Mori headed wide.
Lukaku then danced down the left flank past Tommy Elphick, but saw a low poke at goal smothered away by Federici.
Bournemouth were second-best, but had a golden opportunity to take the lead on 36 minutes when Daniels drove a corner to the back post which hit James McCarthy on the hand.
There were few protests when referee Martin Atkinson pointed to the penalty spot, but Daniels saw his spot-kick beaten away by Robles diving low to his left.
Everton heeded their warning and ten minutes into the second half Barkley collected the ball from Tom Cleverley, set himself and looped a magnificent curling effort over the despairing keeper Federici from 20 yards.
Two minutes later Bournemouth supporters were breathing a sigh of relief when an offside flag ruled out a Lukaku goal.
On 72 minutes Gosling had a golden opportunity to equalise, but, just five yards out, headed the ball harmlessly into Robles’ arms.
But it was big Belgian striker Lukaku who was celebrating the game’s second goal.
Everton won a corner after Eunan O’Kane blocked Barkley’s strike. And Bryan Oviedo’s corner was touched on by Gareth Barry at the near post and Lukaku reacted quickest to fire in the loose ball from five yards.
Bournemouth (4-1-4-1): Adam Federici; Simon Francis, Tommy Elphick, Sylvain Distin, Charlie Daniels; Eunan O’Kane, Juan Iturbe, Dan Gosling, Shaun MacDonald; Junior Stanislas; Joshua King.
Substitutions: Matt Ritchie for MacDonald 63, Glenn Murray for Iturbe 70, Adam Smith for Gosling 76
Substitutes not used: Artur Boruc, Rhous Wiggins, Marc Pugh, Matt Butcher.
Everton (4-2-3-1): Joel Robles; Seamus Coleman, Phil Jagielka, Ramiro Funes Mori, Bryan Oviedo; James McCarthy, Gareth Barry; Aaron Lennon, Ross Barkley, Tom Cleverley; Romelu Lukaku.
Substitutions: Kevin Mirallas for Ross Barkley 80, Oumar Niasse for Lukaku 80.
Substitutes not used: Tim Howard, Leighton Baines, John Stones, Gerard Deulofeu, Leon Osman.
Goals: Ross Barkley 55, Romelu Lukaku 76
Referee: Martin Atkinson
Emirates FA Cup highlights: AFC Bournemouth 0-2 Everton