Henman, the 15th seed, was defeated by the American Jeff Tarango, who caused uproar by walking off court at Wimbledon last year after verbally abusing an umpire. Tarango won 6-1, 6-4, getting the better of a second set which contained four successive breaks of serve.
Rusedski, the 13th seed, hit only two aces with his big serve, but won 79 per cent of his service points and troubled his opponent with low-bouncing backhand slices as he won in just 55 minutes.
"I was pleased with the way I played. I've been losing a lot of close matches," Rusedski, the world No 47, said. "This is a fast court that suits my style."
Henman was not the only seed to make an early exit as Bernd Karbacher, seeded 14th, was beaten 6-2, 6-4 by his fellow German, Hendrik Dreekman. Denmark's Kenneth Carlsen, seeded 16th, rallied for a 5-7, 6-4, 6-2 victory over Yasufumi Yamamoto, a wild card entry.
Pete Sampras - back to No 1 in the world rankings - Michael Chang and Thomas Enqvist, who won the Indian Open on Sunday, are the top three seeds and receive byes into the second round.
In the men's doubles, Britain's Martin Lee and Chris Wilkinson were beaten 6-3, 6-2 by the Americans Jim Grabb and Richey Reneberg.
Belgium's Sabine Appelmans, the women's No 2 seed, was beaten 7-6, 4- 6, 6-0 by Japan's Nana Miyagi. The world No 108 was following up a victory over the Swiss teenager, Martina Hingis, in the Lipton tournament last month.
Romania's Irina Spirlea, the eighth seed, showed athleticism, patience and judgment in beating Mary Pierce, of France, 6-7, 6-4, 6-3 in the final of the Bausch and Lomb Championships on Sunday.
The 22nd-ranked, 22-year-old Spirlea's victory, her third tournament title, moved her to 18th in the WTA rankings in her third full year on the women's tour.