Seth Greenberg calls the Virginia offense "inept" in its Sweet 16 win against Oregon, but credits the Cavaliers defense for stepping up. (0:54)

LOUISVILLE, Ky. -- On a night when both Gene Keady and Ralph Sampson were in the building, Purdue and Virginia each gave themselves a chance to add another long-awaited chapter to their respective program histories.

Purdue blew an 18-point lead to Tennessee in the second half on Thursday, but Carsen Edwards hit two free throws with 1.7 seconds left to send the game to overtime. The Boilermakers pulled away for a 99-94 win in the extra session.

Virginia had a similarly strong finish, holding Oregon without a field goal for the last 5:43 en route to a 53-49 victory.

Now both programs will have the opportunity Saturday night to reach the Final Four for the first time in 30-plus years. Purdue was last in the national semifinals in 1980, and Virginia reached it in 1984.

Kyle Guy celebrates as Virginia advanced on Thursday. AP Photo/Michael Conroy

For Virginia, there's a stark contrast to its NCAA tournament performance from a year ago, when the Cavaliers made history by becoming the first 1-seed to lose to a 16-seed. All season long, Tony Bennett hasn't shied away from what happened, choosing instead to embrace it as a learning experience. Forty minutes from the ultimate redemption story, Bennett is doing much of the same.

"Last year was an amazing year, you know, and then we got to the NCAA tournament, and that was so hard," Bennett said. "And I knew this was gonna be an important year for all of us, in our lives, whatever it brought. And we needed to kind of band together and needed each other to go through it and to respond, up to this point, the way they have -- in the regular season and then to get into the NCAA tournament and be in that spot when we were down 14 and fight, and continue to advance. That stuff will stay with these guys, so again, very thankful, and you know you just want an opportunity and here we are."

Purdue hasn't been at this stage since 2000, but Virginia is on the cusp yet again. The Cavaliers were in this position in 2016, as the 1-seed under Bennett, but were stunned by 10-seed Syracuse and Jim Boeheim.

Given Thursday night's game ended around 12:30 a.m. local time, it's a short turnaround for Virginia to face Purdue on Saturday night -- especially considering Bennett didn't make a single substitution for the final 15:20 of the contest. All five starters played at least 36 minutes.

"We've been preparing for this during the regular season too," junior guard Ty Jerome said. "Coach said he looked at the schedule when it first came out and he saw three Saturday-Monday games. He was upset at first. To start March off, he was happy because it prepared us for this tough team, one day of preparation and another tough team. So we've been preparing for this all season. The ACC did a great job of preparing us for this moment."

The NCAA tournament has continued the tests for Virginia, as the Cavaliers have not made things easy on themselves. They trailed 16-seed Gardner-Webb by 14 points in the first round before cruising to a win in the second half, and then trailed Oregon by three with 5:43 left after Louis King buried a 3-pointer to cap an 11-3 run by the Ducks.

But the Cavaliers locked down the rest of the game, holding Oregon to only four free throws over the final 5:43.

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"We're in March, and it's 40-minute territory, as Coach always tells us," junior guard Kyle Guy said. "So it helps that we try to stay calm under pressure and that we try to execute and get stops defensively, no matter what the score is or how hectic the game is going. That will always be in our advantage, and we're going to try to continue to bring that to every game."

Saturday will be the ultimate test of Virginia's mental toughness. Whether Virginia can truly rid itself of the 16-over-1 demons from last year; whether the Cavaliers can get Bennett over the hump and into the Final Four; and whether one of the best programs in college basketball over the past six years can put its stamp on the sport.

And on the other side will be Purdue and its own Final Four drought, led by a head coach, Matt Painter, who just won his first Sweet 16 game in five tries.

History -- and a trip to Minneapolis -- is on the line.