The British No 2, who lost his chance last week to qualify for next week's ATP Championship in Hannover, won 1-6, 6-1, 7-6. Greg Rusedski was also a winner, beating the Swede, Nicklas Kulti, 7-6, 6-4.
Henman pulled himself together after dropping the first set against Wheaton, whose frequent injuries have dropped him down the world rankings to No 150.
"I felt like I was just going through the motions in the first set," said Henman, who was facing Wheaton for the first time.
"He played well in the first set, but I suddenly felt that I wanted to salvage something from this match. I was disappointed last week in Paris. It was pride of performance for me here."
Henman fought back for two breaks of Wheaton's serve in the second set and had to battle for victory in the third and final set, which featured four breaks of serve in the first six games and finally went to a tie-break.
Henman failed to take advantage of three match points before claiming victory on his fourth with a drop volley, from which the American's lob landed long.
Henman joined Cedric Pioline in the second round, the Frenchman defeating another American, Richey Reneberg, 6-4, 6-4.
The British No 1, Greg Rusedski, has retained his fifth place in the world rankings issued by the ATP Tour yesterday.
The Dutch player Caroline Vis, disqualified from Sunday's Kremlin Cup women's doubles final for insulting the umpire, will also be fined for her outburst, a spokeswoman for the Russian organisers said yesterday.
Vis and her partner, Yayuk Basuki of Indonesia, the second seeds, were trailing 5-3 in the first set to the top seeds, Arantxa Sanchez Vicario and Natasha Zvereva, when Vis argued with the umpire over a line call and was ordered to leave the court.Reuse content