Tulsa (8-4, 6-2 Western Athletic) trailed 26-14 at halftime, but then scored three unanswered touchdowns, including two by Richardson, to take control of the game.
Quarterback Paul Smith, who had replaced injured starter James Kilian in the first half, launched the Golden Hurricane's comeback with a 4-yard touchdown run with two seconds left in the third quarter.
Smith then set up Tulsa's go-ahead score with a 50-yard pass to Montiese Culton, who was brought down at the San Jose State 1-yard line. Richardson scored on the next play with 9:31 left in the game, putting Tulsa ahead 27-26.
San Jose State (3-8, 2-6) lost a chance to gain the lead when a holding penalty nullified Kendrick Starling's 100-yard kickoff return, and Tulsa quickly increased its margin when Richardson scored from seven yards out with 7:05 left.
The Spartans rallied on Lamont Robinson's 1-yard scoring run with 5:59 remaining, but could never retake the lead.
Scott Rislov completed 32 of 48 passes for 470 yards and a touchdown for San Jose State. Lance Martin rushed 24 times for 90 yards for the Spartans.
San Jose State opened the scoring with two first-quarter field goals. After the teams traded touchdowns, the Spartans' Jamall Broussard returned a punt 77 yards for a touchdown and a 19-7 lead.
Both teams scored late in the first half, Tulsa on a 1-yard run by Richardson and San Jose State on a 14-yard scoring strike from Rislov to Tuati Wooden.