The defeat left Chelsea's David Luiz, a boyhood supporter of Corinthians, in tears at the final whistle.
Ryan Giggs gave United a 22nd minute lead before David Luiz equalized from the penalty spot to bring Chelsea level.
The hosts rarely threatened before Clint Dempsey was fouled by David Luiz in stoppage time, only for Cech to keep out the American's spot-kick.
Instead, the final goal was scored by Saviola after David Luiz's long ball had found Di Maria racing past Hibbert for the umpteenth time of the night.
The visitors had been two goals ahead inside 12 minutes as Van Persie's early shot rebounded off a post to hit David Luiz and dribble over the line.
And with the club close to signing Benfica defender David Luiz, the bid for Torres shows that Chelsea are still prepared to use their financial muscle to boost their domestic and European ambitions.
Cech made a fine double save to prevent Chelsea going 3-0 down when he stopped a powerful Rooney effort before springing into action again as David Luiz's misplaced header almost looped into the net.
His team took the lead through an own-goal by Cesar Azpilicueta, then conceded their own by Matthew Kilgallon and then went down to a fortunate deflection by Branislav Ivanovic off a shot by Chelsea teammate David Luiz.
But their Achilles heel this season has been the absence of a sustained cutting edge up front, and so it proved again as Jermaine Beckford struggled to impose himself on a Blues defence missing ineligible new signing David Luiz.
Spanish national team star Juan Mata and Brazilian internationals David Luiz and Oscar have been named to their countries' squads for next month's Confederations Cup in Brazil, meaning they will have to wait another four weeks before finally putting their feet up.
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