Scottie Haralson had 12 points, all in the first half, and Bryson Pope had 11 points and five steals for Tulsa (8-7, 1-1 Conference USA).
"I'm proud of our alertness defensively," said Tulsa coach Doug Wojcik. "(Pope) did a great job and gave the team a lot of energy."
Arsalan Kazemi led Rice (8-8, 0-2) with 14 points and 15 rebounds. Suleiman Braimoh added 12 points.
"This was our worst start of the season," said Rice coach Ben Braun.
"Just way too many turnovers and sloppy passes. You can't spot a good team like Tulsa a lead like that on their home court."
Pope had four steals and five points in the first 99 seconds, helping Tulsa race to a 15-0 lead before Rice broke through on a 3-pointer by Nate Schwarze. The teams battled evenly the rest of the half and Tulsa carried a 35-21 advantage into the break.
Hurtt and Idlet fueled a 14-0 run that pushed Tulsa's lead to 54-33. Hurtt hit a 3-pointer followed by a conventional 3-point play while Idlet had five points in the run.
Tulsa held Rice at bay down the stretch with free throws, making 30 of 36 for the game and 9 of 10 in the final 3:32.
Tulsa shot 47 percent and held Rice to 37 percent. Tulsa finished with a season-high 12 steals while forcing 16 turnovers.
"We came out with good intensity and it carried over throughout the game," said Hurtt, who had scored 20 or more points in his last six games. He led the Golden Hurricane on Saturday with eight rebounds and three assists.