The two goals were not the only big moments in the match as Joel Robles saved Charlie Daniel's first-half penalty with the scores still level. There was no grandstand finish this time and it sees the Toffees reach the quarter-finals of the competition for the fourth time in the last five years.
Robles to the rescue as both sides create limited chances
Roberto Martinez named an unchanged side from the Toffees' 3-0 victory of Stoke City and the 1-0 defeat to West Bromwich Albion last weekend and as Everton did in the two previous matches they started the game confidently.
The Toffees dominated possession in the opening spell of the game but, as on many occasions this season, they struggled to make it count in the final third and failed to create any clear cut chances. Their best chance came just before the half-hour mark when Romelu Lukaku used his pace to get behind the Cherries defence and beat Tommy Elphick to the ball on the left. However, the Belgian could not slide his near post effort past Adam Federici, who saved well from close-range.
Although Bournemouth made seven changes they still possessed an attacking threat, particularly the pace of Juan Iturbe and Joshua King. Iturbe, who joined on-loan from Roma in January, drove forward from inside his own half before cutting in from the right wing; however his effort went wide of the post. However, the Cherries were given an excellent opportunity to take the lead in the 38th-minute.
Joel Robles, who has conceded just once in his last four games since replacing Tim Howard in goal, came to Everton's rescue eight minutes before half-time after Bournemouth were awarded a penalty.
James McCarthy was penalised for handball when defending a cross and Joel read Charlie Daniel's penalty perfectly. The Everton goalkeeper produced a fantastic save, diving to his right, much to the relief of McCarthy and Everton, who celebrated as Bournemouth sent the rebound wide.
Barkley gives Everton the advantage before Lukaku seals the tie
Everton finally found a way through the Bournemouth defence in the 55th minute, and it was a Ross Barkley goal that gave them the advantage in the tie. The England international's shot took a deflection off former Toffee Dan Gosling and looped over Federici and into the back of the net.
Minutes later, the Toffees thought they had doubled their lead, only for Lukaku's goal to be ruled out for offside, although replays suggested that the striker may have been onside.
Bournemouth came close to an equaliser soon after. Junior Stanislas saw his free-kick deflect just inches wide of the target, with Joel left stranded and simply praying that the ball sailed the right side of the post. Gosling then had a great opportunity to bring the scores level, but his free header was straight at Joel.
Ross Barkley should have doubled Everton's advantage, but his effort was deflected behind for a corner when one-on-one. Lukaku did give the Blues some breathing space from the following set-piece.
Bryan Oviedo's corner was helped on by Gareth Barry at the near-post and Lukaku was on hand to hammer home from close range and all but seal the tie for Roberto Martinez's side.
However, Everton knew that the tie was not over until referee Martin Atkinson blew the final-whistle, especially after the last meeting between the two sides in November. On that occasion, it turned out to be a thrilling 3-3 draw, which saw the Cherries score three times in the final 10 minutes.
There was no grandstand finish this time and it sees the Toffees reach the quarter-finals of the competition for the fourth time in the last five years.