The Badgers held John Jenkins (20.1) and Jeffery Taylor (16.3) to 13 and 9 points, respectively, in advancing to face top-seeded Syracuse in the East Regional in Boston.
Jenkins got just one good look at the basket all night, and it came on a wide-open 3-pointer in the final seconds. With the Commodores trailing 59-57, Jenkins created some space between he and Jarred Berggren, but like so many of his other shots on this night, it was long.
"That was as wide open a shot as we gave up the whole game," Badgers coach Bo Ryan said. "It just didn't happen to go down."
Evans grabbed the rebound among a mash pit of bodies pushing and shoving underneath the basket, corralling the ball and drawing the foul with 2.1 seconds left.
"It was a pretty good look," Jenkins said. "I felt like I got a good chance of having it going in, just like a lot of looks I had today. It just didn't drop for me."
Vanderbilt coach Kevin Stallings desperately wanted a whistle on the Badgers but didn't get it.
If the Badgers didn't get away with a foul, they know they got away with a rare defensive breakdown.
"He's one of the best scorers in the country, one of the best shooters in the country," Badgers point guard Jordan Taylor said. "So when you see a guy get a look like that, your heart kind of drops. I know my mom already bought tickets to Boston, so I was hoping that it didn't go in.
"But Jared did a great job of recovering there and making it as difficult as possible. Ryan did a great job of checking out down low and securing the rebound. But it was definitely heart-stopping for a second there."
Berggren would get another chance to come up big for the Badgers, and he did.
Evans sank the first free throw but after a Vandy timeout, he missed the second and the Commodores called another timeout with 1.3 seconds left to set up the full-court play for a chance to send it to overtime.
Berggren got his right hand on Lance Goulbourne's overhand heave, however, and the Badgers, celebrated a return trip to the Round of 16, where they lost last year to Butler.
The fourth-seeded Badgers (26-9) were led by Jordan Taylor's 14 points and also got 12 from Berggren, 11 from Evans and reserve Ben Brust and 10 from Mike Bruesewitz.
The Badgers grabbed two critical offensive rebounds in the final minute. First, Berggren rebounded a miss by Evans with 46 seconds to go and then Josh Gasser, who was hooked up to IVs earlier in the day after waking up sick, grabbed another board with 16.3 seconds left.
He missed the front end of a 1-and-1, however, giving Jenkins the chance in the closing seconds to send fifth-seeded Vandy (25-11) to the regional semifinals for the first time since 2007.
Stifled by a team that allowed just 52.8 points coming in, Vanderbilt didn't take its first lead until the first minute of the second half, on Jeffery Taylor's first basket of the night.
The Commodores actually outshot Wisconsin 43.5 percent to 41.8. But they made just 5 of 19 3-pointers, and the Badgers made 10 of 33.
"Well, people who are going to shoot have off days," said Jenkins, who was 3 of 13 from the floor. "And it was one of mine today, unfortunately."
Jeffery Taylor, had an off day, too. He was just 4 of 12 on the same court where he led Hobbs to the New Mexico state big-schools championship in 2008.
"I think it was more a matter of the ball not going in" than the Badgers' badgering defense, Jeffery Taylor said. "All of my shots pretty much felt good. They just were a little bit short or a little bit too long. Things like that happen in basketball."
Brust's layup and 3-pointer from the right corner gave the Badgers their biggest lead at 53-44 with 6:33 remaining. Suddenly, however, the Badgers had trouble with Vandy's 2-3 zone. They couldn't penetrate and kept taking long 3-pointers with the shot clock winding down.
The Commodores capitalized with a 13-3 run, taking a 57-56 lead on Festus Ezeli's layup with 2:25 remaining.
Jordan Taylor restored Wisconsin's lead with a contested 3-pointer from the top of the circle and the Badgers turned to defense to improve to 4-0 at The Pit. They also won twice here in 2000, advancing to the Final Four.
Ezeli led the Commodores with 14 points but he didn't start and the Badgers took advantage.
Evans started out just like he did in the Badgers' NCAA opener, when he sank his first four baskets and scored nine straight points to give Wisconsin a 14-5 lead on its way to a 25-point blowout of Montana.
This time, he hit a jumper, a 3-pointer and a bank shot from the paint before the Commodores knew what hit them. He then added a free throw that gave the Badgers a quick 10-2 lead.
Ezeli was an onlooker as Stallings started Steve Tchiengang instead. Ezeli entered the game at the 16:50 mark with Vanderbilt trailing 7-2.
Unlike the Grizzlies 48 hours earlier, the Commodores settled down and settled in, pulling to 32-31 at the break on Brad Tinsley's NBA-long 3-pointer at the buzzer.
Jeffery Taylor's minutes were limited in the first half after he picked up two quick fouls and he had no points and one rebound at halftime. He gave Vandy its first lead with a jumper 23 seconds into the second half, but the Badgers responded with seven straight points.
"When you start off the game like that and you have to kind of play spot minutes, it's tough to get into the rhythm of the game," Jeffery Taylor said.
Vanderbilt Commodores guard John Jenkins (23) shoots a three point shot defended by Wisconsin Badgers guard Ben Brust (1) during the first half in the third round of the 2012 NCAA men's basketball tournament at the Pit. (Nelson Chenault-US PRESSWIRE)