The Buckeyes trailed for nearly all of the first 30 minutes before taking control and putting away the plucky Badgers.
"I think the fact that we dug deep as a team shows our poise and shows how tough our team is," said Lavender, Ohio State's junior center and the three-time Big Ten Player of the Year. "And I'm happy we won this game because Wisconsin played an extremely great game."
A trio of threes by three different Badgers helped Wisconsin (21-10) open an early 13-9 lead through four minutes.
After Lavender scored the first two points of the game from the free throw line, Tara Steinbauer put the Badgers on top with a three-pointer.
The Buckeyes (29-4) caught their foes for the first time since the opening minute when Sarah Schulze buried a three from the right wing with about 8:25 to go, but Wisconsin junior guard Alyssa Karel answered right back on the other end when she got loose from OSU freshman Amber Stokes for a trey from deep in the right corner.
Not to be outdone, Prahalis knotted the score again with a three-pointer of her own on the ensuing possession.
A few minutes later, Ohio State looked primed to pull ahead after Hill's old-fashioned three-point play tied the game at 30 with 5:30 to go in the first half, but Teah Gant had other ideas.
The Badger guard scored her team's next seven points during an 11-4 run that gave Wisconsin its largest lead of the half.
Karel scored the last bucket for the run by knocking down a difficult fallaway jumper from the base line that put Wisconsin ahead 41-34 with 1:20 to go.
Then Hill provided the spark again for the Buckeyes as she drove through the Badger defense for a layup and drew another foul, this one on Taylor Wurtz, with 32 seconds to go.
Hill's ensuing free throw was the last point of the half, and her drives would be a recurring theme in the final 20 minutes.
Wisconsin extended to a seven-point lead again early in the second half after Karel made a wide-open three-pointer at the 18:14 mark, but Ohio State quickly erased that.
The Buckeyes tied the game at 46 with three-point play by Lavender at the 15:53 mark, but they couldn't get over the hump until Prahalis canned a three-pointer to give her team a 62-60 advantage.
That prompted a Wisconsin timeout with 9:17 showing on the clock, but back and forth the action continued in front of 7,471 fans at Conseco Fieldhouse.
Lavender gave Ohio State a 73-72 lead with a pair of free throws at the 3:52 mark, then Ohio State did something it had not done much all night: put together three consecutive defensive stops.
At the same time, the Buckeyes stretched their lead to six with a layup by Lavender and an old-fashioned three-point play by Prahalis before Karel ended Wisconsin's scoreless streak by making one of two free throws with 1:34 left.
Unfortunately for head coach Lisa Stone's team, that was the last Badger point.
Hill and Prahalis each hit a pair of free throws to ice the contest and send the Buckeyes to a 4:30 Eastern date with Iowa for the championship game.
The third-seeded Hawkeyes (19-12) advanced to their first final since 2001 with a 59-54 defeat of Michigan State prior to Ohio State's win.
The Buckeyes and Hawkeyes played once during the regular season, an 86-82 barn-burner in Columbus in which Ohio State prevailed.
That Ohio State's semifinal victory ended with a parade to the foul line was appropriate.
The Buckeyes made 34 of 38 free throws, dwarfing Wisconsin's 14-for-19 effort from the line and bringing a smile to the face of Ohio State head coach Jim Foster.
"I think one of the things that this team has done all season long, we really get to the foul line," he said. "We've taken a huge number more foul shots than our opponents have attempted. It's a very, very significant number (139). It's always something that we strive for."
Lavender did the most damage from the charity stripe, making 13 of 16, while sophomore point guard Prahalis was not far behind (11 for 11). Then there was Hill, an athletic wing guard who was 8 for 9. She also added three assists, two steals and a blocked shot in 31 minutes of action.
"She draws contact really well," Prahalis said. "I think she always gives energy, and I think tonight everything she did really helped us."
They needed points from any source they could find because they were matched up with a physical Wisconsin squad that led the Big Ten in scoring defense during the regular season.
"I think Wisconsin came out to play extremely hard," Lavender said. "They were executing extremely well in the first half. Alyssa was hot."
Karel made 10 of 15 field goals and was a perfect 5 for 5 from three-point land. The second-team All-Big Ten performer finished with a career-high 31 points, but she was held without a field goal in the final six minutes.
"We had to figure out a way to get a stop down the stretch," Lavender said. "And I think once we switched up what we were doing defensively, that kind of slowed them down as we got to the one-minute mark, and we pulled through."
Added Prahalis, "We had to stay down on them and get a little more help off the screens, but in the end we got the stops we needed and came out with the win."