The England striker gave a typically spirited performance on a night where defences were on top.
The Red Devils dominated possession and went close through Tom Cleverley, Rooney and Danny Welbeck who arguably missed the biggest chance of the game when he fizzed wide from 10 yards just shy of the hour.
The hosts then had a penalty appeal waved away when the ball appeared to hit Frank Lampard's arm in the area while at the other end Ashley Cole was denied a spot-kick although he appeared to dive.
United continued to press late on but Robin van Persie saw a late volley blocked as David Moyes's first competitive home match in charge ended in a stalemate.
Chelsea's Juan Mata was an unused substitute on the night, which could spark further rumours about his future. Rooney, meanwhile, could yet stay at United after Jose Mourinho appeared to concede defeat afterwards.
PRE-MATCH: Rooney starts. Torres and Mata on the bench for Chelsea - All of the talk leading up to kick off centred around whether Rooney would start and perhaps it was no surprise to see Moyes opt for a big name player on a big occasion. Not to be upstaged, Mourinho sprung his own surprise by picking Andre Schurrle to lead the line ahead of Torres and Romelu Lukaku.
5' FIRST INCIDENT INVOLVING ROONEY - First moment of danger involving Rooney inspires a roar of approval from the home support and is followed by chants of "Rooney, Rooney." This is then echoed by Chelsea's travelling support.
38' CHANCE - Phil Jones drives down the right and fizzes in a low cross that is just about cut out on the stretch. Tom Cleverley follows up and sears a thundering shot just past the upright.
57' CHANCE - Rooney shows great feet to hold off Ramires and slip a disguised pass into Welbeck. The striker has time to create a yard of space but then fires a shot high into the stand from 10 yards out.
71' PENALTY APPEAL - Cole exchanges a one-two with Hazard and nutmegs Jones before tumbling in the area. Again, the ref says no pen. Cole seemed to delay his theatrical fall, with any contact likely to have been outside the box.
77' CHANCE - Rooney links up with Welbeck and then smashes in a 25 yarder that Cech pushes away for a corner.
TALKING POINT: Rooney's future dominated the pre-match but he started, played well and the fans' support of him led Mourinho to say that he thought the England forward would probably now stay at United. Juan Mata, meanwhile, could end up being the mover - he was left out. But with Moyes hinting at a move for Gareth Bale, who knows what will happen next week...
Jose Mourinho has lost just two of his eight competitive games as a manager at Old Trafford (W3 D3 L2).
The stalemate was the first Premier League 0-0 at Old Trafford in 77 games (Arsenal, May 2009).
Petr Cech kept his 200th clean sheet for Chelsea.
MAN OF THE MATCH
Wayne Rooney (Manchester United) - The striker shrugged off speculation over his future to put in a fine display. All that was missing was that elusive goal.
MAN UNITED: De Gea 6, Jones 6, Evra 6, Ferdinand 6, Vidic 6, Carrick 6, Cleverley 6, Valencia 6, Welbeck 6, Rooney 7, Van Persie 7. Subs: Young 6, Giggs 6.
CHELSEA: Cech 6, Ivanovic 7, Cole 7, Cahill 7, Terry 7, Ramires 6, De Bruyne 6, Lampard 6, Oscar 6, Hazard 6, Schurrle 5. Subs: Torres 6, Mikel NA, Azpilicueta NA.
THE MATCH IN A TWEET