"I really didn't care how badly the ankle was feeling," Owens said. "I was going to give it my all and contribute any way I could."
The fifth-seeded Badgers came from 13 points down in the final 4:07.
Wisconsin (24-7) appeared to be out of it after Kevin Johnson hit a three-pointer to make it 58-45, but the Badgers ended the contest with a 16-2 run.
After Tulsa (23-10) was called for a shot-clock violation with 12 seconds remaining, Devin Harris brought the ball up for Wisconsin and dribbled into the right corner.
He kicked the ball to a wide-open Owens, who swished a three-pointer from the left wing to give the Big Ten regular-season champions the victory.
"I just happened to be open on the weak-side wing," Owens said. "When he (Harris) made his move, he drew about three defenders. He made a great pass. I was just ready to catch and shoot."
Tulsa's hopes ended when Jason Parker stepped over the line on the inbounds pass.
"It's really hard to say what happened," senior forward Kevin Johnson said of Tulsa's meltdown. "We just weren't running the offense the way we were. They got a couple steals."
Kirk Penney said Coach Bo Ryan refused to allow the Badgers to give up in the final four minutes.
"It was uncanny," said Penney, who scored only six points. "I looked around in everyone's eyes. Everyone was still believing. Coach was definitely the catalyst in that."
"They made some mistakes defensively," Ryan said. "We got some open looks, did get the clock stopped. Defensively, I said, 'Let's see them make some mistakes.' We had them extended, we tried some run and jump. We don't do it often."
Mike Wilkinson scored 18 points for the Badgers, who will face Kentucky or Utah in the regional semifinals.
Johnson scored 23 points for the Golden Hurricane, who defeated fourth-seeded Dayton in the first round and was the lowest seed team left in the tournament.
"Having that game in our hands and not coming away with the win, it's going to hurt," Johnson said. "There's not much you can say to console us now because we know we had the ability to come away with the win."
Wisconsin, which allowed a Big Ten-low 58.7 points per game during the regular season, got a taste of its own medicine while shooting 35 percent from the field through the first 35 minutes.
But Wisconsin showed some of its trademark defense down the stretch, holding the Golden Hurricane scorelsss for more than three minutes. The Badgers scored nine straight points, closing to within 58-56 on Wilkinson's jumper with 1:13 left.
"We knew we had to get the rebounds, especially at the end of the game, and make them take tough shots," Penney said. "We made them take tough shots and got some turnovers."
Tulsa got its only points in the final four minutes on Johnson's layup with 56 seconds left, but Harris got free for a layup just 10 seconds later.
Wisconsin led for most of the first 16 minutes, but Tulsa ended the first half with a 14-2 run, turning a five-point deficit into a 32-25 lead at the intermission.
Parker's side jumper made it 23-21 with a 4:03 left in the half and ignited the spurt. However, Parker scored only two of his 17 points in the second half.
Harris scored 12 points and Alando Tucker added 10 for the Badgers, who finished at just 39 percent from the field. Wisconsin made six of 22 three-pointers.
Tulsa, which was trying to reach the final 16 for the fourth time since 1997, shot 44 percent.
"We had a great season," Tulsa coach John Phillips said. "But it doesn't feel like it now."