Rooney did not even travel to Merseyside as Sir Alex Ferguson, on the occasion of his 700th Premier League match, claimed he wanted to protect the 24-year-old from abuse from the fans with whom he used to be a favourite.
The disruption appeared to affect his team-mates early on as Everton bossed the opening stages but United were well on top and could have been 2-0 up by the time the Toffees did take the lead through Steven Pienaar in the 39th minute.
Darren Fletcher bagged an equaliser before half-time, however, and goals from Nemanja Vidic and Dimitar Berbatov looked set to earn United a comfortable victory.
However Tim Cahill headed home in the 91st minute to set up a nervy finish and Mikel Arteta fired home from the Toffees' next attack to complete a remarkable turnaround.
Ferguson has overseen plenty of player controversies during his lengthy tenure at Old Trafford but leaving out a player to protect him from opposition fans is unprecedented and surely unlikely to be repeated.
Whether it affected the overall result is open to debate but United found themselves under constant pressure for the first 15 minutes.
Arteta clipped the crossbar with a sixth-minute free-kick and had another shot deflected behind by Jonny Evans, while Pienaar saw his shot from the Spaniard's corner blocked before Leon Osman blazed over all in the same passage of play.
John O'Shea's response was a blistering drive from the left angle of the penalty area which grazed the outside of Tim Howard's left-hand post.
Everton's pressure, albeit slightly less intense, continued while Nani was off the field having a cut lip tended although Cahill, Marouane Fellaini and Leighton Baines all failed to trouble the goalkeeper with half-chances.
There was always the danger their failure to capitalise on possession would leave the way open for United to nick a goal and they almost did in the 34th minute.
Tony Hibbert's foul on Ryan Giggs saw Nani roll the free-kick to Paul Scholes and his powerful drive took a big deflection off Cahill but Howard, diving in the opposite direction, somehow diverted the ball over with his foot.
Four minutes later the American goalkeeper stuck up a hand to palm away Giggs' close-range shot as United counter-attacked.
But the visitors were caught cold shortly themselves when Patrice Evra missed an ambitious overhead-kick clearance to leave Arteta charging through on goal and after he shot straight at Edwin van der Sar, Leon Osman turned the rebound to Pienaar at the far post who rolled home.
Nani's cross was diverted home by Fletcher two minutes before half-time, however, and Berbatov's volley almost put United ahead in added time.
It was apparent at the start of the second half that Everton were in for a tougher test and it took just three minutes for that to become a reality.
Nani's corner from Berbatov's deflected shot was only half-cleared and when Scholes returned the ball to the Portugal international wide on the right he swung over a cross for an unmarked Vidic to head in from five yards.
It at least provoked a reaction from Everton and Pienaar's curling 20-yard shot was held by Van der Sar at the second attempt.
But United were where they like to be, in control and able to counter-attack, with one rapid foray forward seeing Howard deny Nani low to his right.
He got nowhere near the next one in the 66th minute, which owed everything to the brilliance of Scholes and Berbatov.
The former England international's raking pass picked out the Bulgarian wide on the right and his first touch brilliantly took him clear of Sylvain Distin.
With acres of space to run into the languid striker took five or six paces before lashing an early shot into the bottom corner, taking Howard by surprise.
Baines curled a free-kick into the side-netting and as Osman hit a woefully-weak shot at Van der Sar as the hosts tried to find a way back but, as has been the case in their previous matches, they lacked a cutting edge.
However, in a dramatic finish Cahill headed home in injury-time before Arteta's deflected strike snatched an unlikely point.