Last season's runners-up paid a heavy price for the type of defensive blunders they thought they had put behind them and need a draw in their final Group C match at Basel to advance.
Benfica top the group on nine points, level with United and one point ahead of Swiss side Basel who must beat the English champions to progress.
The three-times European champions got off to the worst possible start when defender Phil Jones turned Nicolas Gaitan's left-foot cross into his own net in the third minute.
They pulled one back through Dimitar Berbatov's 30th-minute header and went ahead courtesy of a Darren Fletcher goal in the 59th minute. But another defensive error gifted Pablo Aimar an equaliser two minutes later to send Benfica into raptures.
The Portuguese side are now in pole position to win the group as they host Romanians Otelul Galati, who are yet to pick up a point, in their final game next month.
It is more than they hoped for at the start of the campaign and the delight was evident at the end of the game as coach Jorge Jesus jumped up and down and the noisy Benfica fans lingered at Old Trafford singing and waving their scarves.
"Our main target in the beginning was to get through the group phase and qualify for the knockout rounds," Jesus told a news conference.
"Now it is in our hands to achieve first place in the group. Sometimes it is important [to win the group] in order to avoid teams like Real Madrid and Barcelona."
Group winners will face runners-up from other groups in the last 16.
United, who have featured in three of the last four finals, are now in a more difficult position than they would have wanted thanks to Benfica, who were also the villains the last time the English champions failed to qualify from their group in 2005.
"We didn't deserve what happened tonight," United manager Sir Alex Ferguson told a news conference.
"We did well, it is hard when [you concede] a goal so early in the match. It took us a bit of time to get going again.
"It makes it a bit harder of course [if they qualify as runners-up]."
While Ferguson disagreed with suggestions his side were struggling in Europe, the fact was that both goals they conceded were avoidable.
Having been criticised for poor defensive displays earlier this season, including the 6-1 drubbing by Manchester City in the Premier League, they had tightened up at the back and had just strung together five wins with clean sheets.
Those signs of recovery were undone while some fans were still taking their seats when Jones, not under pressure from any Benfica players, inexplicably directed Gaitan's cross past David de Gea.
Somewhat shell-shocked, United then struggled to impose themselves until Nani's cross found Berbatov's head and the Bulgarian nodded in an equaliser.
United swung the game in their favour 13 minutes after the restart when a wonderful Patrice Evra cross found Fletcher, whose first shot was blocked by Artur before the midfielder stabbed home the rebound.
Celebrations were short-lived, however, with the hapless Jones once again involved in shambolic United defending.
His back pass to De Gea was poorly cleared by the Spanish keeper and the ball came to Bruno Cesar whose cross was not dealt with by United centre-back Rio Ferdinand and the ever dangerous Aimar was on hand to smash in from close range.
Berbatov, selected for a rare start as Wayne Rooney was absent with a hip injury and Javier Hernandez was on the bench, had a golden chance to snatch victory in the 78th minute when he was unmarked with
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