Rooney has been the subject of two failed bids from Chelsea in recent weeks, but he was one of the few impressive players on a night when the season's first major head-to-head clash failed to live up to its billing.
The England striker tested visiting goalkeeper Petr Cech on three occasions, while David Moyes, in his first home game as United manager, saw his side refused a second-half penalty following an apparent handball by Frank Lampard.
The point was enough to send Chelsea top of the nascent standings, but they have played a game more than the rest and United can draw level with them if they win at Liverpool on Sunday.
Rooney's inclusion in United's starting XI, for the first time since April, caused the evening's first ripple of excitement, but Mourinho's team selection was every bit as eye-catching.
The Portuguese named a team without a recognised striker, deploying Andre Schuerrle up front ahead of Oscar, Eden Hazard and Kevin De Bruyne, and leaving Fernando Torres and Romelu Lukaku on the bench.