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.
North Carolina Hall of Fame men's basketball coach Roy Williams is recovering from knee-replacement surgery.
Sparkling facilities are one thing, but Tim Miles needs to regain the momentum of Nebraska's 2014 run to the NCAAs if it is to play with the big boys.
Oregon finished on top of the Pac-12 last season and made a run to the Elite Eight. With loads of talent returning, will the Ducks continue their reign?