Henman, whose lower back problem was aggravated during his straight-sets loss to Fernando Verdasco, of Spain, at Flushing Meadows, New York, has recently spoken ominously about his future as a top-level player.
Dupuis, ranked No 118 in the world, had not taken a set off Henman in their three previous matches and seemed an ideal opponent for the Briton's comeback as a wild card to the tournament he won in 2000.
Henman, ranked No 27, took the opening set with a break in the 11th game, only to lose his own serve at the start of the second set. He responded with two breaks to win his first match since defeating Nicolas Massu, of Chile, at the Cincinnati Masters in August.
"I've been working hard back home and putting in a lot of time on the court and in the gym, but when you step out on the court it is the next level," Henman said.
"Not only was I really pleased with the way I played, I was more interested in how I would feel physically and I feel I came through very, very well. I didn't feel anything. There were no aches and pains, no twinges. The next 24 hours is important, but I do feel confident that I'll react OK.
"I wanted to be very meticulous and disciplined with my service games, and I think I did a very good job. I got a break out of nothing, then the first game of the second set was a lapse in concentration more than anything. But I do like the way I responded from that."
Tomorrow, Henman will play the winner of this afternoon's match between Luis Horna, of Peru, and the Czech Radek Stepanek. Horna won his only previous match against Henman, on clay in the second round at the French Open in June. Henman has won his four previous matches against Stepanek, the most recent having taken place in Key Biscayne, Florida, in March.
Maria Sharapova, the women's world No 1, said at a press conference before the start of the Kremlin Cup in Moscow yesterday that she wanted to play Fed Cup for Russia one day.
"I want to play for Russia," the 18-year-old from Siberia said. "I just don't know when I'll be ready to make my Fed Cup debut."