Having thrown away a winning position to draw at CSKA Moscow in midweek, City was stunned 2-1 by West Ham at Upton Park.
Diafra Sakho's seventh goal in as many games provided fourth-place West Ham with its latest eye-catching scalp while inflicting City's second loss of its title defence.
"I don't think that the team felt what happened on Tuesday in Russia," City manager Manuel Pellegrini said. "Of course I'm very disappointed about the score as I don't think we deserved to lose."
City was dislodged from second place by surprise package Southampton, which followed up its 8-0 rout of Sunderland with a more mundane 1-0 win over Stoke after Sadio Mane's first goal for the south-coast club.
While Southampton's start has been astonishing after a summer of upheaval, Liverpool's has been erratic and epitomized by Mario Balotelli. The striker, whose performance and conduct was decried in Wednesday's 3-0 loss to Real Madrid, failed to score his first league goal for the club in a 0-0 draw with Hull.
But Arsenal hit back after last weekend's draw with Hull to beat Sunderland 2-0 to climb above Liverpool to fifth. Swansea is sandwiched between Arsenal and Liverpool — with the trio all on 14 points — after Wilfried Bony's double clinched a 2-0 win over Leicester.
Leader Chelsea visits eighth-place Manchester United in Sunday's standout fixture. A victory at Old Trafford would put Jose Mourinho's side eight points clear of City after eight games.
City conceded after 22 minutes in east London as Morgan Amalfitano tapped in Enner Valencia's low pass into the box.
West Ham relied on goal-line technology to go further in front in the 75th after Sakho connected with Aaron Cresswell's cross. City goalkeeper Joe Hart initially appeared to have clawed the header off the line but the referee's high-tech aid showed otherwise.
Although David Silva darted past four tackles before slotting past goalkeeper Adrian to pull one back for City, West Ham held on for a third straight home win.
"This is a famous victory for us and one that we will treasure for a long, long time," West Ham manager Sam Allardyce said.
West Ham is two points ahead of London rival Arsenal, which won its first league game in more than a month thanks to another weekend of Sunderland defensive deficiencies.
Alexis Sanchez profited twice. The first time came on the half-hour after defender Wes Brown scuffed a back pass to goalkeeper Vito Mannone. Sanchez went one-on-one with Mannone and lobbed the ball into the net over the advancing goalkeeper.
The Chile forward netted again in stoppage time when Mannone failed to control Will Buckley's back-pass and he was able to tap the ball into the net.
"He took advantage of the mistakes they made, but as well, he has super quality," Arsenal manager Arsene Wenger said of Sanchez. "He has quick feet and that's why he wins many balls that normal players don't win."
The late drama of the day came at West Bromwich Albion where fought back to draw 2-2 at home to Crystal Palace.
Brede Hangeland volleyed Palace in front and Mile Jedinak doubled the London club's lead from the penalty spot before half time. Substitute Victor Anichebe sparked West Brom's comeback at the start of the second half by heading into the net. After Anichebe was fouled by Mile Jedinak, Saido Berahino scored the resulting penalty in stoppage time.