Three days after a 4-0 Champions League defeat at AC Milan that manager Arsene Wenger branded their "worst performance in Europe", Arsenal's sloppiness was back as Kieran Richardson's strike and Alex Oxlade-Chamberlain's own goal sealed their fate.
Sunderland were joined in the quarter-finals by Everton and Bolton Wanderers who recorded 2-0 wins over Championship Blackpool and Millwall respectively, while Norwich City were upset 2-1 at home by second-tier Leicester City.
Chelsea needed Daniel Sturridge's equaliser to force a replay with Birmingham after a draw at Stamford Bridge that did nothing to alleviate the pressure on manager Andre Villas-Boas.
While Chelsea at least stayed in the competition, London rivals Arsenal seem certain to finish without a trophy for the seventh year in a row as their last realistic chance of silverware this season turned to dust against hard-working Sunderland.
Arsenal's day at the Stadium of Light started badly when they lost Francis Coquelin to a hamstring injury with less than 10 minutes gone.
Lacking any sort of attacking spark while looking vulnerable at the back, with Johan Djourou and substitute Sebastien Squillaci short of confidence, Arsenal went behind five minutes before half-time after giving away a free-kick.
Djourou had pulled back Craig Gardner needlessly to concede the kick, which Seb Larsson delivered only for Arsenal to half clear straight into the path of Richardson who blasted the ball into the back of the net thanks to a deflection off Squillaci.
Wenger's side, who last weekend came from behind to beat the same opponents 2-1 in the Premier League, allowed their hosts to go further ahead in the 78th minute when Oxlade-Chamberlain sent the ball into his own net after Larsson had hit the post.
"We have to take the critics on board and stay together and face the critics. There is only one response in our job at the club - to stay united and fight and focus on the next game," Wenger told a news conference.
But facing a mountain to climb to overturn their Champions League deficit and trailing Premier League leaders Manchester City by 17 points, Arsenal's search for a first trophy since they won the FA Cup in 2005 is set to continue for another year.
'POOR RESULT'
The picture is only marginally more positive for 2010 winners Chelsea, who went behind to an under-strength Birmingham team when David Murphy scored before levelling when Sturridge climbed to head in Branislav Ivanovic's 62nd-minute cross.
Chelsea squandered an earlier chance to level straight after Murphy's opener when Juan Mata's penalty was well saved by diving Birmingham goalkeeper Colin Doyle and home fans expressed their unhappiness by chanting ex-manager Jose Mourinho's name.
"It is a poor result of course," said Villas-Boas who added he had the "unconditional" support of owner Roman Abramovich.
"But it was an excellen
