Rusedski looked on course for victory when he won a tie-break in Tuesday's first set but his big serve then became erratic and the American fought back to win 6-7, 6-3, 6-4.
Rusedski's defeat means that Tim Henman is left to carry Britain's hopes in the event and the Wimbledon quarter-finalist is now due to meet the Russian Yevgeny Kafelnikov.
Pete Sampras, the world No 1, joined Courier in the third round after a 6-3, 6-4 win over Jakob Hlasek of Switzerland. It was the American's first match since he lost to Richard Krajicek, the eventual champion, in the quarter-finals at Wimbledon.
Monica Seles, the top seed, also put her Wimbledon disappointment behind her when she avenged her defeat by Katarina Studenikova at the All England club by thrashing the Slovakian 6-2, 6-0 in the second round of the Canadian Open in Montreal.
Seles, who is still troubled by a shoulder injury, said she would decide about having an operation after the US Open. Jennifer Capriati, the former prodigy who is attempting another comeback, rediscovered her old form as she won a baseline duel with the 11th-seeded Romanian, Irina Spirlea, 6-4, 6-2.
Boris Becker, who has not played competitively since being forced to withdraw from Wimbledon with a wrist injury, has pulled out of next week's New Haven tournament in Connecticut. The German faces a battle to be fit for the US Open starting on 26 August.
Jeremy Bates, who announced his retirement at this year's Wimbledon, is to take up a coaching position with the Lawn Tennis Association next week.Reuse content