The 41-year-old Clemens gave up two singles and a solo homer to Henry Blanco, walked just one and set a season high for strikeouts.
With career victory No. 317, Clemens (7-0) moved within one of Phil Niekro for 14th place all-time.
Clemens has won all seven of his starts and allowed more than one run just once. His start is the best by an Astros pitcher since Juan Agosto began the 1988 campaign 10-0.
Clemens, whose best start was 14-0 in 1986, has won 10 straight decisions dating to last season and is 66-20 since July 2, 2000. The six-time Cy Young Award winner improved to 3-0 in five career regular-season starts against Florida.