The 32-year-old, playing in his last major tournament, prevailed 6-4 3-6 6-3 6-4 against the 27th seed to reach the second round in New York.
Having snatched the first set, Henman looked short on energy in the second but he dug deep against a player he had beaten only once in six matches.
And the Briton closed out the fourth set in style to seal an unlikely win.
"I've been on the receiving end of defeats by him in the other Slams," said Henman.
"The whole nature of the match, not only the level of play but the support, the atmosphere out on a big court, it was fantastic.
And Henman, who will retire after next month's Davis Cup tie against Croatia at Wimbledon, added: "If I had lost in straight sets today I don't think it would have been the biggest deal in the world.
"But having said that, to play against him of all people, having lost to him on four or five occasions and play that well, it's great. It certainly leaves a good taste and it's definitely something I can build on.
"When you say I've got nothing to lose and everything to gain, I think that's spot on. I feel like I want to play these last two events and give them everything.
"If I do play well and go out on a high, whatever that means, it will mean a lot to me. But, on the other side of the coin, if I hadn't won today and things didn't go according to plan at the Davis Cup, it's not suddenly going to tarnish my career in any way, shape or form.
"So I think with that attitude it could bode pretty well."
Henman, a former US Open semi-finalist, will face 22-year-old Frenchman Jo-Wilfried Tsonga in the second round.
He will head into that encounter with renewed confidence after coming through a match which he had started as a huge underdog.
Federer is way better HHH
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