Milos Uzan scored 12 points, Le'Tre Darthard scored 11 and Sam Godwin added 10 points and six rebounds for the Sooners (13-1).
Otega Oweh, Oklahoma's top scorer for the season, didn't make a field goal. But he scored seven of his eight points on free throws in the final 4:39 to help the Sooners win the kind of close game that often escaped their grasp last season.
"I just think it's a completely different team than last year," Uzan said. "We've got a lot of older guys that have been in situations like this before. Last year we struggled closing out games. So I think for us to close this game, was a big, big jump for us."
Oklahoma coach Porter Moser liked the way his team gutted out the victory. The Sooners had averaged 82.5 points for the season, but they won this one with grit and toughness instead of explosive scoring.
"I think Iowa State's one of the best teams in the country," Moser said. "I mean, they're so hard to score against. They're so physical and they do it in a basketball fundamental way — the way they switch, the way they hedge, the way they guard you (on) the ball. It's just so fundamentally physical."
Hason Ward, Milan Momcilovic and Robert Jones each scored 12 points for Iowa State (11-3). The Sooners held Tamin Lipsey, Iowa State's scoring leader at 15.5 points per game entering the day, to four points on 1-for-10 shooting.
Iowa State had won six straight, all by double digits. The Cyclones, who entered the day averaging 86.2 points per game, shot 42.6% from the field, including 3 of 16 from 3-point range.
Iowa State led 58-57 before Oklahoma seized control for good with a 7-0 run that included three assists from McCollum. First, there was a dunk by Godwin to put Oklahoma ahead. Darthard's 3-pointer with just over three minutes remaining put the Sooners up 62-58. On Oklahoma's next possession, with the home crowd standing, Godwin scored a layup to push the lead to six and force an Iowa State timeout.
"Javian's a great point guard," Uzan said. "He's out there making the right plays as well. I think they were so pressed up on him and he was able to make the right reads late in the game which was big time for us."
Iowa State's overall strong defense wasn't good enough in the closing minutes.
"We believe in what we do defensively, and we've got to trust that down the stretch because we didn't get timely stops and obviously, that's where they gained the separation," Iowa State coach T.J. Otzelberger said.
Oklahoma led 32-26 at halftime. Lipsey had two points on 1-for-6 shooting, and Iowa State made just 1 of 8 3-pointers before the break. It was just the second time this season Iowa State failed to score at least 30 points in the first half.
Iowa State scored the first six points of the second half to tie the game at 32 before Oklahoma responded with a 3-pointer by McCollum.
Iowa State's Ward missed a free throw, then ran in, leaped up to collect the bounce and threw down a powerful two-handed dunk in traffic that cut Iowa State's deficit to 37-34. The game see-sawed from there.
