Danuel House had 11 points for the Cougars (2-0), who protected their late lead by going 8 for 10 from the line in the last 46 seconds.
Houston led 44-26 at halftime, but a 17-6 run brought San Jose State to within 69-64 with 1:08 remaining. But with the Spartans forced to foul, the Cougars capitalized.
Brandon Morris had 10 points, and Thomas added 10 rebounds for Houston.
Chris Cunningham scored 15 points for San Jose State.
After a season that saw his shooting numbers slip, should Nigel Hayes return for his senior year at Wisconsin or take the gamble to put him name in this year's NBA draft?
Isaiah Taylor talks about his decision to declare for the NBA draft and what he will miss most about Texas.
Chattanooga women's basketball coach Jim Foster has received a one-year contract extension, the same day the school gave the men's coach a two-year extension.