United recovered from Phil Jones's third-minute own goal when Dimitar Berbatov headed in Nani's cross.
Darren Fletcher then ghosted in to prod past Artur to make it 2-1, but Pablo Aimar equalised from close range.
Berbatov and Rodrigo both had late chances to win it but were off target.
The United forward's chance was the better one as he volleyed over from Fabio's centre 12 minutes from the end.
But although Sir Alex Ferguson's side were without the injured Wayne Rooney, they will be frustrated to have thrown away a lead having worked so hard to establish themselves in the game.
Fletcher's goal on 59 minutes came after a sustained period of pressure on the visitors' goal, but Benfica's equaliser a minute later followed a poor clearance by United goalkeeper David de Gea.
The result means Benfica have already qualified, and United will need to better Benfica's efforts against Otelul Galati in the last round of games if they have any hopes of topping the group.
Still, the hosts may be content with the draw on a cold night, as they looked partially frozen when Benfica went ahead with a rapier-like attack.Continue reading the main story Man Utd will qualify if they get a point at BaselThey can top the group if they better Benfica's result against Otelul GalatiIf Benfica win against the Romanian side they top the groupBasel can still qualify if they beat Man Utd
Nicolas Gaitan, who has impressed in Portugal this season, was fed down the right and when he checked back onto his left foot, his cross hit Patrice Evra before Jones deflected into his own net.
Old Trafford was stunned but the fans began to shake off their disbelief when Nani went on several trademark dribbles, and Ashley Young had a shot saved.
Gaitan and Aimar were joining the Benfica midfield to run rings around Michael Carrick and Fletcher, but once United improved their passing out of defence, they started to create problems for the visitors.
Berbatov was playing in front of Young and was largely anonymous before he equalised.
And although there was a suggestion of offside to his header from Nani's centre, it was a fine strike as he notched his first Champions League goal since 2008, and his second this season.
The Bulgarian almost set up Young for a second moments after scoring, but Benfica keeper Artur produced a decent stop and Aimar was also denied by De Gea in a frantic five minutes.
United maintained their high tempo at the start of the second period as Young's shot was blocked by the impressive Ezequiel Garay, before Fabio tried to chip Artur.
With the pressure building on the Benfica defence, the hosts took the lead when Fletcher arrived in the box to poke in Evra's cross at the second attempt just before the hour.
That should have settled Ferguson's men with Carrick beginning to produce some clever passes, but their advantage only lasted a minute.
De Gea's short kick fell to Bruno Cesar, who dribbled into the United box and crossed for Aimar to equalise despite Rio Ferdinand's attempt to clear.
It would have left Ferguson fuming after his side had worked so hard to turn the game around, and the Benfica goal once again knocked United's rhythm.
With parity restored, Jorge Jesus's team began to show the same confidence they had in the first 15 minutes, although Berbatov could have had a second when he volleyed over from 10 yards.
Perhaps United would have been satisfied with the result after Rodrigo went close in the dying stages, but they can afford to show little of the same carelessness when they travel to Switzerland to face Basel.