curling delivery narrowly missed Jonny Evans and David Luiz before nestling inside Cech's far post.
As Old Trafford resounded with joy, Chelsea briefly sprung into life. Evans was required to block Moses' 20-yard effort and Frank Lampard fired straight at David De Gea after neat approach work from Mata.
That was a mere blip in United's control of the half, however. An incisive move down the right flank between Rafael, Rooney and Nani culminated in the latter crossing for Chicharito to stab a left-footed effort just wide of Cech's near post.
Chelsea's goalkeeper was then called into a fine double save: first he blocked Rooney's shot with his legs, then he reacted brilliantly to tip the ball over the bar after Luiz miscued his clearing header and sent it on target.
The first period drifted to a close with little by way of noteworthy goalmouth action, though there was an enforced change of personnel as Nani made way for Antonio Valencia through injury.
Though United began the second period in no apparent distress, Chelsea soon set about turning the tie on its head. The 52nd-minute double substitution of Hazard and John Obi Mikel for Lampard and Moses gave the visitors momentum, and before the hour mark they halved United's advantage.
Again Mata was involved, cutting infield and ferrying the ball to Hazard, and the Belgian curled a quite magnificent effort inside De Gea's far corner with virtually no backlift.