City, who move to a new home next season, produced a dazzling display which belied their lowly league standing as they made it three league wins in a row.
"I enjoyed it more than any other derby I have been involved in, and I think we thoroughly deserved our victory," enthused KeeganWhile City had plenty to celebrate it was a sorry story for the Reds Devils, even though this was their first defeat in seven Premiership matches.
Sir Alex Ferguson's side, who last lost to City in 1989, were completely out-played with their defensive display a shambles.
And on the evidence of this display it is hard to see them mounting a championship challenge while City should have no problem staying up.
City took the lead in the fifth minute after Phil Neville's poor pass resulted in Rio Ferdinand being dispossessedFabien Barthez could only parry Goater's weak shot and Anelka fired home the rebound from four yards.
United quickly drew level when Ryan Giggs set up Ole Gunnar Solskjaer who slid in to score from six yards.
City ought to have finished the half further ahead when Anelka was clean through on goal, but was brilliantly denied by Barthez.
A third goal came shortly after the re-start after Phil Neville gave the ball away in midfield.
Eyal Berkovic released Goater who held off a challenge from Laurent Blanc to slot the ball home.
United rarely threatened though they twice linked close in dying minutes when Ruud Van Nistelrooy was brilliantly denied by keeper Peter Schmeichel and John O'Shea sliced a shot wide from two yards with the goal at his mercy, a miss which just about summed up United's afternoon