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.
Gonzaga has signed California transfer Jordan Mathews to a financial aid agreement for the 2016-17 season.
Coach Gilmore on CWS win: 'It's indescribable' Coastal Carolina head coach Gary Gilmore reflects on his 21 years as head coach and is proud of how far the program has come.
Two late June events provided a great start on the 2020 class and a look at some new 2019 talent.