Martin O'Neill's side joined their near neighbours Newcastle in falling at the third round, while Jon Walters bounced back from his horror show against Chelsea to book Stoke's passage through against Crystal Palace.
FA Cup round-up: Fulham leave it late for win over Blackpool as Sunderland crash out
Sunderland crashed out of the FA Cup to Bolton Wanderers after losing their third-round replay 2-0, while Fulham celebrated the narrowest of narrow escapes against Blackpool.
Martin O'Neill's side has enjoyed an upsurge in Premier League fortunes in recent weeks, moving six points clear of the relegation zone, but they joined north-east rivals Newcastle United in falling at the first hurdle in the cup.
England Under-21 striker Marvin Sordell was the match-winner at the Reebok Stadium, scoring twice in the space of nine second-half minutes to secure Bolton a home tie against Everton in the fourth round.
His first goal arrived from the penalty spot in the 64th minute after a foul on Darren Pratley by Jack Colback, before he dispatched a Tyrone Mears cutback in the 73rd minute to complete the scoring.
"This is a big club and we shouldn't be spending 40 years without winning something, we really shouldn't," said Sunderland manager Martin O'Neill.
"I know some people field weakened sides but we didn't. We tried to win tonight and we weren't able to do it, and that was very disappointing."
On the prospect of a meeting with Everton, Bolton coach Dougie Freedman said: "We're looking forward to it.
"We feel right now that we can perform against anyone, and if we defend like we did tonight and keep our discipline, we have definitely got every chance."
Fulham were on the verge of elimination to Blackpool after on-loan Aston Villa forward Nathan Delfouneso put the hosts 1-0 up in the 82nd minute at Bloomfield Road.
However, a stunning 25-yard strike by Kieran Richardson in the last minute took the game to extra time and Fulham skipper Brede Hangeland scored the winner with four minutes left to secure a 2-1 win.
"I had him (Richardson) on the bench so if something went wrong I could bring him on, and he did that," said Martin Jol, the Fulham manager, afterwards.
"It is always a relief. To see us come back 30 seconds from the end, and to score the winner was ... they couldn't score the winner, so you knew the one who scored first would win the game and luckily it was Fulham."
Fulham will now meet either Manchester United or West Ham United, who lock horns in a replay at Old Trafford tonight.
Jon Walters went some way towards atoning for his horror show in Stoke City's 4-0 loss to Chelsea at the weekend by scoring twice as Tony Pulis' side saw off Crystal Palace 4-1 after extra time.
Walters scored two own goals and missed a penalty in Saturday's game but he netted twice in extra time on his return to the Britannia Stadium, after Glenn Murray's 87th-minute penalty for Palace cancelled out Kenwyne Jones' opener.
Cameron Jerome claimed a late fourth for Stoke, who will tackle English champions Manchester City for a place in round five in what is a repeat of the 2011 final which City won.
"I wasn't going to play Jon tonight - I had decided on Friday that I would give him a rest," Pulis admitted afterwards.
"But then after what had happened on Saturday, I decided the best thing to do was to get him out there again.
"And scoring the goals and playing the way he played, I think it's just great for him."
Chelsea, meanwhile, will face a trip to third-tier Brentford in the fourth round after the League One outfit saw off Southend United 2-1.
In the only all-Premier League encounter of the evening, Queens Park Rangers put their relegation fears to one side to win 1-0 at West Bromwich Albion through a 75th-minute header by Jay Bothroyd.
Wigan Athletic avoided an upset as Mauro Boselli's emphatic 18th-minute strike gave them a 1-0 win at home to third-tier Bournemouth, who twice hit the frame of the goal.
Former Senegal star El-Hadji Diouf celebrated his 32nd birthday by scoring the decisive goal from the penalty spot as Leeds United won 2-1 at Birmingham City to set up a home tie with Tottenham Hotspur.
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