Rusedski beat the Ukrainian 7-6, 6-4 in an hour and a quarter, after Henman had beaten the higher-ranked Spaniard Felix Mantilla 6-4, 4-6, 6-4.
There were no breaks of serve in the first set before Rusedski, the world No 4, won it on a tie-break with his third set point. He had already saved three set points himself before Medvedev dumped a second serve return into the net.
The British No 1 then broke serve in the ninth game of the second set and won on his third match point.
Earlier, Henman, ranked 21 in the world, eased through the first set, but struggled in the second as the Spaniard, the world No 14, began to pull out some excellent passing shots.
Henman served three double-faults in the sixth game of that set, which he duly lost, and it looked then as if the British player was on his way out. But, in the final set, Henman took the game to Mantilla, producing a wide variety of shots, which led to him breaking the Spaniard's serve in the seventh game.
This proved crucial as both players held serve for the rest of the match, Henman eventually clinching victory on the first of his three match points.
"I was very happy with my game up until 6-4, 3-2. But then I made three double-faults and gained just one more game in the set,'' Henman said. "I knew he had had all his best results on clay and I knew he was a very solid player."
Henman now meets Sweden's Jan Apell, who is ranked 727th after three shoulder operations kept him out of the game for more than a year.
The French Open champion, Gustavo Kuerten, became the third seed to be eliminated when he lost 6-4, 6-4 in the second round to Czech Bohdan Ulihrach yesterday. The hard-court tournament has already lost its two top seeds, Yevgeny Kafelnikov and Sergi Bruguera, in the first round, leaving Rusedski and Goran Ivanisevic as the favourites.
Kuerten, 21, the fifth seed and world No 11, was visibly exhausted from his three-set battle against Spain's Albert Costa on Tuesday - his first match since injuring his ankle at the Grand Slam Cup in Munich.
Chris Wilkinson lost his second-round match in the Singapore Open yesterday. The British No 3 was beaten 6-4, 6-3 by the rising German player, Nicolas Kiefer, but was not downhearted by the result.
"The tournament is going fine and I am playing well. British tennis is getting better all the time and that's a credit to everyone involved in the game," he said.
"Tennis is pretty much an open sport at the moment. Even here we have seen No 1 seed Michael Chang and Mark Woodforde both go out at the first- round stage."
Wilkinson will be looking for further success in the doubles tournament where he has reached the quarter-finals with the American David Wheaton.
Wilkinson will be involved in the British National Championships in Telford next month and expects the success of Britain's top two players to inspire a host of youngsters to come through in years to come.
"The success of Tim Henman and Greg Rusedski has been a great inspiration for the youngsters in this country," he said. "It's been great for the British team and other players are doing well on the back of their success."Reuse content