Still, Reese connected on eight of his 15 shots, including 6-of-8 from beyond the arc for Tulsa (23-9).
"I was fortunate to get the opportunity to make shots, and I was able to do it," Reese said.
Ben Uzoh added 14 points and and seven assists, while Justin Hurtt finished with 10 points for the second-seeded Golden Hurricane.
Jerome Jordan, Tulsa's leading scorer (14.7), scored only six points but grabbed nine rebounds.
Connor Frizzelle scored 10 points for 10th-seeded Rice (10-22), which defeated Marshall 60-59 in Wednesday's opening round. Rodney Foster, Rice's leading scorer (12.1), was limited to eight points on 1-of-5 shooting from the field, and six points from the free-throw line.
The Golden Hurricane were shooting at a 55 percent clip (11 of 20) with under seven minutes left in the first half. Reese would end the half leading Tulsa scorers with 11 points, helping the Golden Hurricane to a 41-17 halftime lead.
"We were real anxious," Uzoh said. "Emotionally, we were high. We had a lot of energy, and it showed by getting off to a great start."
The Tulsa defense, with Reese guarding Foster, clamped down on the Owls. Rice missed nine of its first 10 shots and committed nine early turnovers, allowing Tulsa to go on the 21-0 run.
"I liked our team better in the second half than I did in the first," Rice coach Ben Braun said. "I thought, defensively, (Tulsa) dug in really hard in the first half. We became a little stagnant. They took advantage and knocked down some shots."
The game got intense with 13:24 remaining when Rice's Lawrence Ghoram stole the ball at midcourt and was driving for a layup. Tulsa's Bishop Wheatley was in pursuit and, when Ghoram went up, Wheatley grabbed his right arm, sending him hard to the floor.
As officials were calling an intentional foul on Wheatley, Rice's coach came charging off the bench along the baseline toward Wheatley before he was restrained. Ghoram was helped from the floor and, after reviewing the play, officials amended the call to a flagrant intentional foul and ejected Wheatley.
C-USA officials said the flagrant foul doesn't draw an automatic rejection, but they will review the play to see if any further action against Wheatley is warranted.
Braun said Ghoram seemed fine and there was no evidence of nerve damage, but they will take X-rays to see if there is any fracture.
Rice's coach said he still didn't see the point with Tulsa holding a big lead.
"I was just disappointed that type of foul took place," Braun said about the play that got the Rice coach fired up. "I subscribe to the (theory) that you don't have to have some common sense about what you do on a breakaway with somebody
Rice shot 36 percent from the field in the game (18 of 50), and struggled from beyond the arc, hitting only two of its 12 shots.
The biggest success for Rice in the game was a strategy of double-teaming Jordan, a first-team all-conference selection, in the low post. But that allowed Uzoh to penetrate and dish outside to Tulsa's Reese.
The one-sided scoring early on gave the Golden Hurricane a 25-3 lead, and coach Doug Wojcik was able to rest starters Uzoh, Jordan and Reese. Wojcik knows the benefit of pacing his team through the tournament.
Last year, the Golden Hurricane had to play four games in four days, including two in overtime. By the time they reached the championship game against Memphis, Tulsa had run out of gas.
"We had a big lead and tried to take some minutes off (key players)," Wojcik said. "We knew what it was like last year.
"We tried to stretch it out as much as we can."