Haas faltered in the first set, getting shutout in a tiebreaker, before rallying for a 6-7 (0-7), 7-6 (7-3), 6-4 win over sixth-seeded Radek Stepanek.
Second-seeded James Blake easily handled qualifier Bjorn Phau, 6-4, 6-1, in his Tuesday match while fourth-seeded Mikhail Youzhny breezed by Dmitry Tursunov, 6-3, 6-1, and No. 5-seeded Marcos Baghdatis, a runner-up at the Weber last year, advanced with a 6-4, 7-5 win over Jan Hernych.
World No. 1 Roger Federer, coming off being routed in the French Open final, is the top seed. He bypassed the Weber last year after winning the tournament each year from 2003 to 2006. Third-seeded Tomas Berdych is the defending champion.