Henman, the 15th seed and British No 1, lost 6-3, 6-3 to the Ukraine's Andrei Medvedev, who also beat him in last month's Davis Cup tie between the two countries.
Henman, No 18 in the world, made 31 unforced errors in his 67-minute match. Rusedski was beaten 1-6, 6-3, 7-6 by the big-serving American Jonathan Stark, who he had beaten in five sets at Wimbledon last month.
Last week Henman lost in a first-round match in the Canadian Open to a little-known Canadian qualifier, Sebastien Leblanc.
"I didn't expect him to return that well," Henman said. "My serve was patchy, but I was serving as big as I could. After last week I was eager for a win that I could get under my belt. This is very disappointing."
Rusedski had spent a few days last week practising in Florida with Pete Sampras. But the skills of the world's best player did not appear to rub off on the adopted Briton against Stark.
Rusedski was playing his first match after three weeks out through injury. Britain's No 2, picked up a groin strain during the Davis Cup victory over Ukraine last month.
Rusedski, who beat Stark last year in South Korea, was also troubled by his injury when he was beaten on clay by Sweden's Magnus Larsson in the second round at the Mercedes Cup in Stuttgart two and a half weeks ago.