Kelsee Grovey also finished in double figures with 14 points.
Mayberry went 6-of-16 and hit 5-of-8 free throws while Brady, a sophomore from Healdton who went on a 3-point rampage late in the game, hit 7-of-9 including four treys.
It was also a career-best for Brady.
Mayberry, along with fellow seniors Tiffani Couisnard, who was named to the Conference USA Women’s All-Academic Team earlier in the day, and Jessica McQuinn were honored after the game on Senior Night.
“I look at all three of our seniors at what they’ve given to this program,” Tulsa coach Matilda Mossman said. “And with the coaching change, how they accepted us and allowed us to coach them, I couldn’t be prouder of them as human beings. All three are bright and intelligent young ladies and have a great future ahead of them.”
“It is bittersweet,” said Mayberry, who played her last game at the Reynolds Center. “Tulsa has given me so many memories. I’ve never regretted the decision to come here. I went through a lot of adversity here. It has helped me grow, not only as a player, but as a person, tremendously. I will miss this place a lot.”
Yasmee Thompson led the Cougars with 17 points, Marche’ Amerson scored 16 and Porsche Landry finished with 12.
Tulsa shot 45 percent (26-of-58) in field goals, 50 percent (8-of-16) outside the arc and 70 percent (16-of-23) in free throws.
The Cougars (13-16, 7-9) won the rebounding battle, 44-33, but shot 40 percent (24-of-60), 35 percent (7-of-20) in 3-pointers and was 50 percent (8-of-16) in foul shots.
The Golden Hurricane (13-16 overall, 8-8 in C-USA) only trailed Houston (13-16, 7-9) twice and that came early in the game. There were two ties in the first half after the Cougars came back with some runs.
The Hurricane owned a 32-30 halftime advantage, then gradually broke away in the second half.
Brady nailed a pair of 3s, one from each corner, bringing the score to 51-39.
But Houston would cut into the lead again, it drew to within four points twice. A layup in the paint from Porsche Landry brought the score to 57-53 with 8:09 remaining.
But a 16-3 spurt, including 3s by Grovey and Brady on back-to-back possessions brought the score to 73-56 with 3:46 left.
It was Tulsa’s largest lead of the game.
The Golden Hurricane now move on to the Conference USA Tournament, which takes place Wednesday through March 16 at the Convention Center in Tulsa.