The west London club took the lead in the 19th minute when Lewis Holtby’s pass was steered home by Steve Sidwell.
You can have as much possession as you like, we should have scored more
The Red Devils looked to be heading for three points when they scored twice in 80 seconds through Robin van Persie and Michael Carrick.
But Bent headed in a 94th-minute leveller to earn the Cottagers a draw and heap further misery on United boss Moyes, whose side now trail fourth-placed Liverpool by nine points.
“It’s been a bit like that this season” said Moyes. “Today was as bad as it gets. We dominated the game. Being one down was bad enough.
“The amount of attempts, chances and play we had was unbelievable. How we didn’t win I have no idea.
“It’s goals that count. You can have as much possession as you like, we should have scored more.
“You’ve got to try and keep making it work. The payers tried that today and eventually the goals did come and I was more disappointed we didn’t make it 3-1.
“It was a bit of carelessness at the back and we could have cleared the ball but didn’t and it cost us.”
Meanwhile, Sidwell could not hide his joy at the final whistle after helping Fulham earn a famous draw.
“It’s a massive point, I’m speechless really,” Sidwell said. “We put a lot of effort in and rode our luck but came away with a point.
“It was hard. It’s never easy coming here so hopefully we can kick on now for the rest of the season. We had chances to put it to bed in the first half and I thought we deserved a point.”
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