Phil Bardsley had opened the scoring for the Wearsiders before Tim Cahill’s opportunist strike restored parity for the Toffees.
The home side bombarded Simon Mignolet’s goal but were unable to produce a winner thanks to some fine saves from the Belgian.
David Moyes made six changes to the side humbled at Anfield on Tuesday; with Steven Pienaar cup-tied, Royston Drenthe started for the Toffees.
Nikica Jelavic made his second start for the club at the expense of Denis Stracqualursi, while Phil Neville, Johnny Heitinga, Leon Osman and Tim Cahill were all named in the starting XI.
Unsurprisingly Martin O’Neill stuck with the same team that recorded an impressive 1-0 win over Liverpool a week ago, with Nicklas Bendtner shaking off a knee injury to partner Fraizer Campbell. Lee Cattermole and Stephane Sessegnon missed out through suspension.
A ferocious atmosphere at Goodison Park saw a strong start from the hosts, with both Osman and James McClean coming close in the first three minutes, but both headers were steered off target.
Referee Andre Marriner was in the thick of the action early on, first turning down Everton appeals for a penalty after Drenthe was upended by Craig Gardner, and then awarding Sunderland a free-kick for what seemed a fair challenge from Leighton Baines.
From the resulting free-kick, Jack Colback opted to play the ball short to an unmarked Bardsley, who unleashed a thunderbolt that flashed past Tim Howard before nestling in the corner of the American’s net, sending the 6,000 travelling Macams into raptures.
Chants of ‘We’re all going to Wembley’ from the Sunderland fans were soon extinguished by the home side as they hit back immediately.
Good work from Drenthe down the Everton left allowed Baines time to measure a cross. The England international picked out Jelavic who nodded his effort towards goal, only for Cahill to instinctively divert the ball past a helpless Mignolet.
Having notched his eighth career goal against the Wearsiders, Cahill threatened to grab his ninth just 10 minutes before the break.
From a Baines corner, the Australian produced a trademark leap to tower above Michael Turner, but his header was well saved by Mignolet under pressure from Heitinga.
The home side again came close to taking the lead as Drenthe’s free-kick clipped the woodwork on its way over, but O’Neill’s men survived the onslaught and entered a well-earned break on level terms.
Everton began the second-half as they had ended the first, with Mignolet twice preventing Cahill from doubling his afternoon’s account.
As the visitors offered little in response, Moyes’ men continued their relentless assault on the Sunderland goal, with Jelavic again dominating in the air but seeing his header land agonisingly on top of Mignolet’s goal.
Substitutions from both managers disrupted the flow of play a little, as the game threatened to head harmlessly towards a draw, with both sets of players seemingly paying for a frantic first-half of football.
With just five minutes to play David Moyes had one last roll of the Everton dice, introducing Stracqualursi.
It was, however, his strike partner Jelavic who almost had the last word, as Mignolet produced a stunning save from Heitinga’s header before jumping to his feet to deny the Croatia international and ensure the two teams must now do it all again at the Stadium of Light to determine who will appear at Wembley.
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