The Sooners (2-1) broke the school record for consecutive wins on Owen Field by holding opponents scoreless in back-to-back games for the first time since 1987.
Ryan Broyles caught a career-high 11 passes for 128 yards and three touchdowns, and Brandon Caleb emerged as a potential second viable target with 104 yards on five catches and two scores.
Jones finished with 336 yards on 25 for 37 passing with two interceptions. His first pass was intercepted after it tipped off of Broyles' hands, but Tulsa went three-and-out and just kept squandering opportunities early.
The Golden Hurricane (2-1), boasting the nation's top offense the past two seasons, ran 31 of their first 33 plays in Oklahoma territory but came away without a point to show for it. Tulsa got the ball inside the 15 on two of its first four possessions, only to have quarterback G.J. Kinne turn it over both times.
Brian Jackson picked off Kinne's pass into the end zone intended for Damaris Johnson the first time, and Jeremy Beal forced him to fumble on a sack the second time. Kinne, making his third career start after transferring in from Texas, also threw an interception late in the first half.
Each time, Oklahoma marched the opposite way for a touchdown. Caleb got behind the defense for a 63-yard touchdown catch, twice stiff-arming Kenny D. Sims as he raced down the Sooners sideline to make it 17-0. DeMarco Murray followed that with a 13-yard score, spinning twice along the same sideline before leaping for a frontward flip into the end zone.
Broyles scored the Sooners' final three touchdowns, twice catching short passes and then knifing his way through the defense and then getting open deep for a 36-yard TD pass. That one pushed Jones past the previous school record of five touchdown passes held by Bradford, 2003 Heisman winner Jason White and 2000 Heisman runner-up Josh Heupel.
It's too early to know how long it will be before Jones gets a chance to follow up his record-setting outing. That will depend on whether Bradford, who's out with a sprained shoulder, is able to come back in time to face Miami on Oct. 3 after Oklahoma's week off.
Jones remained in the game until the Sooners' final possession, with only 95 seconds left, as most of the rest of the offensive starters came out. Oklahoma's defensive starters also stayed in for the duration, keeping the shutout intact.
The team's last back-to-back shutouts came against North Carolina (28-0) and Tulsa (65-0) in the second and third games of Barry Switzer's next-to-last season as the Sooners' coach. Tulsa was shut out for the first time since 2004 against Navy.
Kinne completed 12 of 26 passes for 106 yards but got replaced after Oklahoma made it 45-0 with just over 8 minutes left in the third quarter. Jacob Bower and Shavodrick Beaver split the rest of the Golden Hurricane's snaps except one, when Kinne returned and fired a pass directly to Sooners linebacker Travis Lewis, who dropped it.
The longest previous home winning streak for Oklahoma started with Bud Wilkinson's fourth home game as head coach in 1947 and stretched until 1953.