On-loan DaMarcus Beasley trotted from the bench and galloped through the hapless Hammers defence to give Stuart Pearce a winning return to Upton Park.
City's Team USA substitute struck seven minutes from time to send his side soaring into the top half of the table and leave worried West Ham going into 2007 trapped in the bottom three.
Coming into this crucial match, five points and five places had separated these two sides and Alan Curbishley would have given anything to swap positions with counterpart Pearce.
Following the dismal defeat against Portsmouth on Boxing Day, the new Hammers boss was without suspended duo Paul Konchesky and Nigel Reo-Coker, and that meant recalls for Christian Dailly and Lee Bowyer, while skipper Teddy Sheringham replaced out-of-form top-scorer, Bobby Zamora.
Buoyed by the three points collected at Sheffield United on Tuesday, 13th-placed City made just one enforced change as Stephen Jordan came in for the suspended Hammers transfer window target, Joey Barton.
Although Hayden Mullins, Bowyer and Sheringham aimed innocuous efforts in Nicky Weaver's direction during a disappointingly subdued opening 45 minutes, the visitors - who had managed just eight goals on their travels - also caused few problems in Robert Green's penalty area.
But in terms of festive fare, this really was the cold left-overs and, with the crowd already pleading for Carlos Tevez to be unleashed from the bench, Jonathan Spector - who had earlier been booked for tripping Hatem Trabelsi - summed up a dismal, goalless, first half with a 20-yard scuffed effort that flew towards the corner flag.
Ten minutes after the break, the crowd finally got their wish as Tevez replaced the anonymous Matthew Etherington and, on the hour, the City faithful also raised their first cheer of a rain-soaked afternoon when Micah Richards tried his luck with the visitors' first effort of the day.
Typically, that flew high and wide and, with neither keeper seriously under any threat, both red-faced managers tried to up the stakes with the introductions of Carlton Cole plus Beasley and Georgios Samaras.
With 13 minutes left, Tevez almost repaid the fans' faith in him when he let fly with a dipping 20-yarder that just cleared the diving Weaver's right-hand angle. But that was the closest West Ham were to come to scoring.
And, with just seven minutes remaining, the fresh legs of Beasley - on loan from PSV Eindhoven - carried him between Spector and Dailly, before drilling an unstoppable 12-yarder between Green and his left-hand post to give City an unlikely victory and leave the flustered and frustrated Curbishley wondering just why he has decided to return to management.