Chelsea's troubles deepened as Rafa Benitez's side lost at West Ham in the Premier League on Saturday, while Manchester United took advantage of Man City's slip-up to extend its lead to three points.
United twice came from behind to win 4-3 at Reading after City had drawn 1-1 at home to Everton.
Chelsea is already 10 points behind United after a 3-1 loss at West Ham left the European champions without a win in seven league matches, three since Benitez replaced the fired Roberto Di Matteo as manager.
Tottenham is now only behind Chelsea on goal difference in fourth place after beating Fulham 3-0.
Arsenal dropped to 10th after Michu's double gave Swansea a 2-0 victory at Emirates Stadium.
Queens Park Rangers remains winless and bottom after being held to a 1-1 draw by Aston Villa. West Bromwich Albion dropped to fifth after being beaten 1-0 by Stoke, and Liverpool defeated Southampton 1-0.
Liverpool's former manager, Benitez, is enduring a miserable return to the league he left in 2010 with the fans against him and the team not performing.
Chelsea took the lead at West Ham in the 13th minute when Fernando Torres cut the ball back from the right to Juan Mata, who swept in his eighth goal of the season.
The hosts fought back in the second half, with former Chelsea striker Carlton Cole equalizing in the 63rd minute after taking the place of the injured Andy Carroll.
Cole set up Mohamed Diame's decisive goal for West Ham in the 86th before being replaced by Modibo Maiga, who added a third in stoppage time.
"We could have finished the game in the first half, but it was totally different in the second half," Benitez said. "We didn't start well, they were on top of us and we couldn't manage ... we gave the ball away easily, weren't comfortable in possession."
And the fans made their opposition to Benitez clear with "Rafa Out" banners and chants backing Di Matteo.
At Arsenal, manager Arsene Wenger also faced jeers from his own fans and the team's title hopes faded further.
Swansea went in front in the 88th when Michu broke free after a neat one-two with Luke Moore and slotted the ball into the net.
In stoppage time, the Spaniard latched onto a long clearance and raced through to again beat goalkeeper Wojciech Szczesny, prolonging Arsenal's worst start to a league season since Wenger arrived in 1996.
"It is a good moment to stick together," Wenger said. "I am not so much worried about (league) places, even if that is not the place you want to be. But I believe what is important is we get the quality of our game back. Then the places change."
United was forced to come from behind to win for the seventh time in 15 league matches this season.
All seven goals at Reading came in a 26-minute frenzy, starting in the eighth minute by Hal Robson-Kanu putting the hosts in front from close range.
Anderson equalized after a one-two with Ashley Young, and Wayne Rooney put United in front from the penalty spot after Jonny Evans had been brought down by Jay Tabb
But then corners from Nicky Shorey were headed in by Adam Le Fondre and then Sean Morrison to give Reading a 3-2 advantage.
Rooney began United's second comeback by slotting the ball into the net from Patrice Evra's cross and then setting up Robin van Persie to put United in front for good.
"We're needing to rescue the situation all the time," United manager Alex Ferguson said. "Fortunately, we have players who can do that."
Tottenham had no trouble overcoming Fulham to record a third staight win. Sandro put Spurs ahead 10 minutes into the second half with a 35-yard strike, before Jermain Defoe scored twice in five minutes.
At Etihad Stadium, Marouane Fellaini headed Everton in front in the 33rd, but managed to concede a penalty before halftime after tangling with Edin Dzeko.
That allowed Carlos Tevez to equalize from the penalty spot and preserve City's unbeaten start to the season.
Liverpool recorded only its second win in seven league matches after Daniel Agger headed in his first goal of the season just before halftime against relegation-threatened Southampton.
West Brom dropped to fifth after ninth-place Stoke inflicted a second successive loss, with Dean Whitehead scoring a late goal.