Phil Bardsley opened the scoring with his first goal of the season as Sunderland started the brighter, only for Tim Cahill to level for Everton midway through the first half.
Everton boss David Moyes showed where his priorities lay as he brought in all the key players he had rested for the midweek Premier League defeat at Liverpool. Cahill, Nikica Jelavic, Phil Neville, Leon Osman and Royston Drenthe all returned to the starting line-up.
Sunderland were without the suspended Lee Cattermole, but Nicklas Bendtner was passed fit and started up front with Fraizer Campbell.
In Cattermole's absence, a fired-up Drenthe had plenty of joy surging through the centre of the pitch, whilst young Irish winger James McClean continued to impress on the left for Sunderland.
McClean and Osman both sent early headers off target, before Drenthe had a strong appeal for a penalty turned down by referee Andre Marriner after the Dutchman appeared to have been tripped just inside the box by Craig Gardner.
Sunderland took the lead on 12 minutes after a clever free-kick caught Everton off guard. Sebastian Larsson placed the ball and it was squared early to Bardsley by Jack Colback. The right-back drilled home a decent low effort from 20 yards which beat Tim Howard for his first ever FA Cup goal.
Cahill then equalised with only his second goal since the start of 2011. Good work from Drenthe allowed Leighton Baines to cross for Jelavic. The Croatia striker's header was weak, but Cahill was well placed to nod the ball past the wrong-footed Simon Mignolet.
After the break Everton, roared on by the Goodison crowd, emerged as the side more likely to win on the day. Seamus Coleman drilled a strike into the side-netting after forcing his way between two Sunderland players before Jelavic had a decent header land on top of the net.
The Toffees then had another solid shout for a penalty refused when John O'Shea's hand was raised as Jelavic headed the ball against it, but again the officials let play continue.
Mignolet's heroics for Sunderland in the closing minutes ensured they will have to do it all again on Wearside. Everton sent in a free-kick from deep and Johnny Heitinga's header was palmed away by the diving Belgian, who then sprang back to his feet to deny Jelavic's effort on the rebound at the near post.
In total, Everton had 19 shots to Sunderland's five over the 90 minutes, but in truth defeat for either side would have been harsh. There will now be another 90 minutes, and perhaps extra time and penalties, standing between one of these sides going to Wembley.