With the scores locked at 2-2, Kompany's scuffed his clearance into the path of Philippe Coutinho, who thumped the ball past City goalkeeper Joe Hart for the game's fifth goal.
Before then, City had fought back from going into halftime 2-0 down to draw level at 2-2.
The first-half belonged to the rampant hosts - and Raheem Sterling. The diminutive attacker sent the Reds ahead inside the opening ten minutes as he bamboozled both Kompany and Hart inside the City penalty area before driving home.
The match turned on it's head after the break following James Milner's introduction. The England midfielder created David Silva's first and had a hand in the Spaniard's second, which is likely to be recorded as an own goal.
At 2-2, it was City's points to claim until their captain's amazing blunder handed Coutinho and Liverpool a shock winner.
Jordan Henderson saw red in injury-time for a nasty tackle on Samir Nasri. But it did little to affect the final result.
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