Henman, so uncertain whilst narrowly escaping two days previously against the Czech Daniel Vacek, played with increasing assurance to overcome the New Zealander Brett Steven 6-4, 6-4 on Thursday, while Rusedski was at his ferocious best in overcoming the top 20 Spaniard Albert Costa.
The British No 2 looks to be heading for a top 20 place himself for the first time after a 6-3, 7-6 win in which he produced 15 aces and some fierce commitment. Rusedski will now meet the 1996 Wimbledon men's singles champion, Richard Krajicek, today. Henman's win has earned him a repeat of last year's famous match at Wimbledon against Yevgeny Kafelnikov, who is the top seed.
At the RCA Championships in Indianapolis, the world No 1, Pete Sampras, suffered a surprise third-round defeat to Magnus Larsson, losing 7-6, 4-6, 7-6.
Andre Agassi produced his best tennis for six months as he saved three set points before berating beat the third seed, Alex Corretja of Spain, 7-6, 6-1. Seven of the top eight seeds have now been eliminated.