After surprise defeats to Aston Villa and Crystal Palace in recent weeks, Chelsea again stuttered against weaker opposition, as Jose Mourinho's 77-match unbeaten home run as Chelsea boss came to an end in a major boost for league leader Liverpool.
Chelsea could not hold onto its lead after Samuel Eto'o opened the scoring, as Connor Wickham levelled from a rebound six minutes later following Marcos Alonso's long-range effort. Fabio Borini then scored from the spot after Cesar Azpilicueta brought down Jozy Altidore in the box with eight minutes remaining.
Elsewhere, Crystal Palace claimed a fifth consecutive win with a 1-0 defeat of West Ham to secure its place in the topflight next season, and Swansea secured a vital 2-1 win at Newcastle that piled more pressure on Magpies manager Alan Pardew.
Peter Whittingham's second-half penalty gave Cardiff a precious point in a 1-1 draw against Stoke, and Aston Villa could record only a goalless home draw with Southampton.
Sunderland goalkeeper Vito Mannone made 14 saves as Chelsea blew the opportunity to dislodge Liverpool from top spot. The Reds will have the chance to extend their lead to five points at Norwich on Sunday.
After holding Manchester City to a draw midweek, Gus Poyet's players were again the party-poopers. The Black Cats took four points from their last two games and are just three points from safety.
"With Sunderland this year, anything can happen," said Poyet, a former Chelsea player.
With three matches to go and a potential title decider at Anfield next weekend, Mourinho's side can't afford any more slip-ups in its quest for a fourth Premier League crown.
After Eto'o put Chelsea in front, Schwarzer —who replaced Petr Cech after the Czech keeper was ruled out by a virus — could only parry Alonso's effort away and the ball came back straight to Wickham, who made no mistake from the rebound.
Chelsea players showed their frustration and midfielder Ramires hit Sebastian Larsson in the face with an elbow before Altidore went down under Azpilicueta's challenge. On-loan Liverpool player Borini kept his head cool to score the resulting penalty
"When I went to take the penalty I thought 'goal.' That's why we take penalties, because you're confident," Borini said. "We showed great character and belief."
Mourinho and his staff were not happy with the referee after the penalty decision and assistant coach Rui Faria was sent to the stands. Mourinho had to drag Faria away from fourth official Phil Dowd as the hosts' protests turned bitter.
"His performance was unbelievable and when referees have unbelievable performances it's fair to congratulate them," Mourinho said ironically about referee Mike Dean. "He came here with one objective, the objective to make a fantastic performance and he did that."
Against Newcastle, Swansea striker Wilfried Bony scored twice to take his goal tally for the season in all competitions to 22 as his team moved six points above the relegation zone with three matches left.
Newcastle remained in ninth place despite its calamitous run of five consecutive losses but fans are showing increasing anger, with growing calls for Pardew to step down as manager.
In Cardiff, Whittingham's 50th-minute goal cancelled out Marko Arnautovic's penalty — the first spot-kick Cardiff has conceded this season — that was converted during the dying seconds of an otherwise forgettable first half.
Cardiff remains stuck in the relegation zone, two points adrift of possible safety.
With its fifth consecutive league win — a feat it did not achieve since December 1992 — Palace is mathematically safe from relegation. But included in that streak is a 3-0 win at Cardiff on April 5, a match which is the subject of a league investigation: The Welsh club claims Palace obtained its lineup before the game.
Tottenham kept its small hopes of a top-four finish alive and dented Fulham's survival ambitions with a 3-1 win over its London rival. Spurs are four points behind fourth-place Arsenal, though the Gunners have played one game less.