Cambridge twice battled back from behind to condemn 10-man Stockport to a seventh consecutive away draw.
The Hatters took an early lead when striker Nick Chadwick headed home from John Miles' free-kick.
Luke Berry equalised for the hosts with a fine finish from the edge of the area before substitute Danny Whitehead nodded the visitors ahead once more.
Jordan Patrick levelled from a tight angle after Carl Piergianni saw red for a second bookable offence.
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Cambridge United manager Jez George told BBC Radio Cambridgeshire:
"I don't think we started the game very well, obviously the early goal doesn't help.
"That's two games running we've done that, so it's disappointing, as were the nature of the goals.
"We did improve and we started passing the ball and when we did that we looked dangerous and created some decent stuff."