Broyles finished with 13 catches for a school-record 217 yards, including a 57-yard touchdown grab midway through the second quarter. The catch broke former Purdue standout Taylor Stubblefield's record of 316 receptions - Broyles finished the game with 326 in his career.
The senior from Norman, Okla., added another TD catch in the fourth quarter, giving him 44 for his career. He came into the game tied with former Oklahoma State star Rashaun Woods for the Big 12 mark.
Dominique Whaley added 165 yards rushing and a touchdown, and Michael Hunnicutt hit all four of his field-goal attempts for the Sooners (6-0, 3-0), who didn't put away the Jayhawks (2-4, 0-3) until Broyles' second touchdown catch with 10:22 remaining in the fourth quarter.
James Sims and Darrian Miller combined to rush for 141 yards and two touchdowns for Kansas, but Jordan Webb endured constant pressure and finished 13 of 25 for 108 yards. He was sacked five times and KU didn't score after halftime.
Oklahoma, coming off a 55-17 Red River rout of Texas, may have been looking for some style points against the nation's worst defense with the initial BCS standings due out Sunday.
Instead, it had to settle for slogging to a lackluster victory in a game that didn't end until 11:58 p.m. local time. About half the announced crowd of 42,580 was around at the end.
Jones missed on his first four passes against a defense that surrendered 56 points in the first half alone last weekend against Oklahoma State. But the junior quarterback got on track quickly, hitting his next two pass attempts to Kenny Stills. The second was a 17-yard touchdown pass that gave Oklahoma a 7-0 lead with 11:32 left in the first quarter.
Hunnicutt's 36-yard field goal made it 10-0 later in the quarter.
Kansas center Jeremiah Hatch was hurt on the ensuing possession when he was blocking down field on a short pass completion. Hatch was immobilized and removed from the field on a stretcher, but returned to the stadium and was walking on the sideline by the end of the game.
On the first play after Hatch was hurt, with the Jayhawks facing fourth-and-1, Webb pitched the ball to Sims around the corner and he went untouched 56 yards for a touchdown.
Whaley fumbled early in the second quarter but Kansas could only manage a tying field goal, and Roy Finch capped a nine-play, 70-yard drive with an 8-yard run that made it 17-10.
The Jones-to-Broyles connection really got going after that.
After catching a few short passes on the perimeter, Broyles went flying downfield on a post route and Jones hit him in stride for his record-setting reception. The touchdown made it 24-10.
Kansas answered with Miller's touchdown plunge moments later, but Hunnicutt added another field goal just before halftime and two more in the third quarter to make it 33-17.
Broyles finally put the game away when he got wide open and hauled in a 43-yard pass with 10:22 left in the game that put the Sooners ahead 40-17. Whaley added the exclamation point when he scored from 10 yards out in the closing minutes.