Here are the main talking points from the Toffees' cup triumph including just how important will Joel Robles penalty save prove to be to Everton's season.
Martinez rewarded for fielding strong side
It is now expected for managers, particularly Premier League clubs, to rest their best players for domestic cups and use their strength in depth. Bournemouth made six changes, Arsenal made nine and Hull City made 10.
Everton supporters may be losing patience with Roberto Martinez, but the Toffees boss deserves credit for fielding a strong side against Bournemouth. Martinez named an unchanged side from the team that beat Stoke City 3-0, before losing 1-0 to West Bromwich Albion last weekend.
The defeat to West Brom left his side six points behind the European spots and his selection suggested that the trip to the South Coast was a challenge from which progression was a necessity. His decision to select a strong side would have heartened supporters of the competition and Evertonians.
Martinez's team selection was ultimately rewarded with passage to the quarter-finals of the competition. Everton were dominant and controlled the game for the majority of the 90 minutes and Bournemouth boss Eddie Howe said after the match that "Everton had a bit more quality in the end."
How important will Joel's penalty save prove to be?
The tie could have turned out completely different for Bournemouth had Charlie Daniels converted his first-half penalty, which was superbly saved by Joel Robles. Not only do moments like this prove to be turning points in matches, but they can also prove to be turning points in a season.
When James McCarthy was penalised for handling a Charlie Daniels corner inside the area, the obituaries for Everton's season - and Martinez's position - seemed easy enough to write. However, Joel's save may have just given Everton's a much needed kiss of life.
Against a much-changed Bournemouth side, Everton were struggling for inspiration but Joel's heroics handed them a lifeline and not only proved to be a key moment in the match, but could be a moment of inspiration that will be looked back on as a turning point that was more significant than most others.
This result meant more than simply progressing into the next round of the competition, it is about the momentum it can offer the final third of the season and the hope that this will not be another campaign consigned to a file labelled 'one to forget'.
No grandstand finish this time
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 after the Toffees led 2-0.
This was not the only occasion where the Toffees have thrown a two goal lead away this season; they repeated the feat against Chelsea just six weeks later. It prompted questions concerning Everton's ability to see out a match and defend winning positions, but there was no grandstand finish this time.
Everton showed plenty of nous as they confidently saw out the remainder of the tie without any real problems and exactly what impact this game will have on the Toffees' season remains to be seen.
Anywhere but home in the next round?
Roberto Martinez would have been pleased to have avoided the likes of Arsenal, Manchester City and Manchester United in the last round and a favourable last-eight draw could quickly open up a semi-final spot for Everton and a trip to Wembley.
The Everton boss has said that he would favour a home tie in the next round, but the time when visiting teams used to a dread a trip to Goodison Park has vanished. Last weekend's 1-0 defeat to West Brom was their sixth home defeat of the season, while the Blues have now lost only two of 19 away games in all competitions.
In fact, the Toffees have been defeated just once in their last 13 away games in the FA Cup - the 2014 quarter-final defeat at Arsenal, however Goodison Park in an FA Cup quarter-final is a different story.