Price had some key steals in the second half as Oklahoma overcame a sluggish start and then held off a second-half charge by Colorado (14-13, 5-11).
"To go 13-3 and 24-4 against the schedule we've played, I couldn't be more ecstatic," Oklahoma coach Kelvin Sampson said. "I thought the (Big 12 South Division) portion of the schedule was a lot tougher this year, but we are second to the No. 1 team in the nation (Kansas).
"We didn't win the Big 12 championship, but these kids are champions."
Quannas White, Aaron McGhee and Jason Detrick each had 12 points for Oklahoma.
James "Mookie" Wright had 16 points for Colorado, which has lost six of seven, while Michel Morandais had 14, Nick Mohr 13 and Blair Wilson 10.
Oklahoma made just five of its first 21 shots as Colorado frustrated the Sooners with 2-3 zone defense.
The Buffaloes built a 13-6 lead with 12:45 remaining on a 3-pointer by Wilson and a transition jumper by Morandais. Colorado led 22-17 when the Sooners went on a 14-1 run, fueled by Price's 3-pointer and a layup after a turnover. Oklahoma led 40-31 at halftime and stretched it to 59-47 before Colorado got within 66-61 on a 3-pointer by Wilson and a layup by Mohr.
Colorado trailed 70-64 after David Harrison made one of two free throws with 7:26 remaining, but Price stole the ball from Mohr and made a layup to give Oklahoma an eight-point lead with 6:45 to go. It was one of three turnovers by Mohr in the stretch.
"We knew that if we played off him, he'd be a great passer. He had 11 assists and no turnovers against Texas A&M," said Price, who finished with five steals. "We wanted to pressure him because we know he's not as quick as Wright."
Oklahoma put the game away with consecutive baskets by White and a baseline jumper by reserve Daryan Selvy after a Colorado turnover.
"At the end of the game I thought they gave us every chance," Colorado coach Ricardo Patton said. "But we ran out of bodies, and free throw shooting hurt us."
Colorado was 7-for-16 from the line in the first half, while Oklahoma was 10-for-10.
Four Buffs played 34 minutes or more, and Stephane Pelle, their second-leading scorer, got in foul trouble. He was limited to 20 minutes and scored just seven points, half his average. Seven Sooners played 22 minutes or more and an eighth was on the court for 12 minutes. Patton feared Oklahoma's depth might be a decisive factor.
"They've got guys who can hurt you at every position," he said. "Their depth certainly hurt us down the stretch."
The Sooners shot 57.1 percent from the field in the second half and were 17-of-19 from the free throw line for the game, including making their first 15.