The winner Monday will be the first Big 12 team to reach the Final Four.
"We're three games from the championship," said All-American swing guard Stacey Dales, who scored 15 points. "This is a stage where we haven't been before. The sky is the limit."
The Sooners (30-3) also got 18 points and 40 minutes from LaNeishea Caufield and Rosalind Ross scored 15, all in the second half. Oklahoma struggled in the first half and trailed 30-27 at halftime.
"Everybody did what they needed to do in the second half," Hill said. "Rosalind started making her 3s, LaNeishea hit some awesome shots and the rebounds were just coming to me."
Even more impressive, Oklahoma inflicted so much damage with only six players.
"We had lots of opportunities tonight to go with a small lineup," Sooners coach Sherri Coale said. "We've got four of the best guards in the country and it helped us to make some mismatches."
Oklahoma used a 14-3 run over a span of 2:33 to break away from a 38-all tie. Dales had eight points in the spurt, including a steal that led to a three-point play and a 3-pointer that made it 50-41 with 11:30 remaining.
"We had them in pretty good shape in the first half, but we took some ill-advised shots early on in the second half," Tech coach Marsha Sharp said. "A team as good as Oklahoma makes you pay for that."
The Lady Raiders (20-12) made a few runs, but nothing strong enough to reclaim the lead. Oklahoma beat Tech for the third time this season, the fifth in a row and sixth in the last seven meetings.
"We really felt that we could win this game," Sharp said. "There were comments in the paper that we were just happy to be here. That wasn't really the way we felt. We really felt we could win."
Tech freshman center Cisti Greenwalt scored 18 points and had eight rebounds in her first NCAA tournament game, while Jia Perkins scored 15 and Amber Tarr had 12.
It was a big night for Hill, a 6-foot-1 forward who played with her parents and sister, Boise resident Kirsten Heffner, in the stands. She had seven points and eight rebounds by halftime.
"She usually has to travel to Oklahoma to see me," Hill said.
That wasn't good enough for the lead at the break, however. Tech led 30-27 at halftime after Greenwalt scored 10 points on 5-of-7 shooting and the Sooners shot 33 percent and committed 14 turnovers.
"We couldn't get the same production in the second half," Sharp said. "They changed their defense and started fronting our post players, and we weren't able to adjust."
Oklahoma regrouped in the second half, shooting 53 percent to pull away.
"In the first half, people were trying to take it upon themselves to get it going," Caufield said. "In the second half, we went to our strength. We came together as one."
It was a breakthrough win for Oklahoma, which is within a game of joining the men's team in the Final Four. The program was dropped in 1990, then revived and brought to national prominence by Coale.
The Sooners almost made it last year but went down in the third round under similar circumstances. Assigned to the West region, they played a late-night contest against Washington and lost after spending the whole day too geared up for the game.
This time, they've tried to stay loose and had fun.
"It was mental preparation, knowing that this isn't just like any other game because it's three hours later than we usually play," Hill said. "Last year, we were unprepared and tight."
They're planning a scavenger hunt at a Boise mall where they'll take pictures of selected items. Dales also said they were inspired by Sarah Hughes' exuberance after winning a figure skating gold medal at the Olympics.