Manchester City lost its top spot in the Premier League to rival Manchester United after a shock 1-0 defeat at Swansea on Sunday.
Luke Moore scored with a powerful close-range header for the Welsh side in the 83rd minute as City, unbeaten in the league at home, lost its fourth away match this season after failing to penetrate the notoriously stingy Swansea defense.
Man United beat West Bromwich Albion 2-0 to move first - one point ahead of City.
''We need to start scoring again, and we are in second position now. The lead can change every game but it is important to start winning and scoring again,'' City manager Roberto Mancini said. ''All the players in this moment are tired, but we have a lot of energy to go top again and there are 10 games to play.''
City's Micah Richards had a goal called back for offside in the dying minutes of the game at the Liberty Stadium.
Joe Hart saved a penalty from Scott Sinclair in the seventh minute after the England goalkeeper was judged to have brought down Wayne Routledge.
Yaya Toure was caught in possession by Gylfi Sigurdsson and Swansea coolly put Routledge down the right to deliver a cross that Moore headed beyond Hart's dive. The goal triggered all-out attack from City and Swansea goalkeeper Michel Vorm made an acrobatic save to deny Kolo Toure's effort.
City thought it had salvaged a point when Richards headed in as Vorm came and failed to reach a cross, but the fullback was ruled offside.
Sinclair almost added a second in added time as Swansea broke after Hart had gone up for a corner, but his strike from halfway came up short of the line as the 'keeper recovered.
Mancini's side had topped the table after each round of fixtures since October and would have stayed there on goal difference with a draw.
Newly promoted Swansea moved ever closer to survival, with a 14-point gap to the bottom three all but guaranteeing the team another season in the Premier League. It has conceded only 10 goals at home in the league this season, the best record apart from City (6) and Liverpool (10).
Swansea had already beaten Arsenal at home and drawn with Chelsea and Tottenham this season, and was keen to make up for its 4-0 loss at Man City at the start of the season.
Sinclair should have given Swansea a seventh-minute lead after referee Lee Mason adjudged Routledge had been felled by the advancing Hart and awarded a penalty.
But the winger failed to find the net from the spot for the first time this season as Hart saved the tame effort low to his right.
City had spent the majority of the opening 20 minutes penned in their own half, aside from a brief breakout that saw Mario Balotelli show nice footwork before Steven Caulker made a vital challenge as the Italian shaped to shoot.
Balotelli was cutting an increasingly frustrated figure and he let it show as he attempted a shot from near the touchline on halfway which flew well wide of the goal.
Mancini removed Gareth Barry after 37 minutes to bring on Sergio Aguero.
And the Argentine's introduction heralded City's best spell of the half as Yaya Toure's volley was deflected over by Sigurdsson's block, before his brother Kolo headed off target and David Silva drilled a shot wide just before the break.
City continued to press at the start of the second half and Aguero failed to make the most of a good chance as he shot wide when Balotelli picked him out after cutting out Caulker's lazy pass.
It was Swansea's turn to go close moments later as Danny Graham's ball across the six-yard box almost found Joe Allen's run, with Kolo Toure diverting it to safety.
City felt it should have had a penalty on the hour mark when Balotelli went to ground easily with Allen in close attendance.
Vorm then made a sharp save to deny Richards after Silva had tricked his way into the box.
Caulker flashed a header across the face of goal from Sigurdsson's corner while Hart made easy work of a weak shot from Routledge as Swansea lifted the heavy pressure they had been under.
And the Swans then stunned the visitors as they snatched the lead with just seven minutes to go.
''We were clearly the better side throughout the game,'' Swansea manager Brendan Rodgers said. ''We retained our positivity and when we had to defend, we defended well.''
