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.