Salt Lake City ? If it turns out to be the last win at Indiana for Mike Davis, it might be his sweetest, too. And maybe his most unlikely.

With his team outplayed on almost every level, the Hoosiers’ lame-duck coach had every reason to believe he’d be packing it up for good Thursday night after the first round of the NCAA Tournament.

His players weren’t quite ready to say goodbye, though. And when Robert Vaden hit the go-ahead 3-pointer with 3.3 seconds left, Indiana was on its way to a thrilling, come-from-behind victory, 87-83 over San Diego State.

“It didn’t cross my mind about this being my last game,” Davis said. “All I was thinking about was making sure my guys fought to the end.”

They did, and came out on top in a sloppy, exciting, gut-wrenching game for Indiana’s soon-to-be-former coach.

The sixth-seeded Hoosiers (19-11) won despite letting 11th-seeded San Diego State (24-9) shoot 56 percent and despite getting outhustled, outsmarted and outplayed by the Aztecs for 39 minutes-plus.

Mohamed Abukar led San Diego State with 24 points. Marcus Slaughter had 13 points and 10 rebounds, but it wasn’t enough to help the Aztecs win the first NCAA game in school history.

“These are hard, hard losses,” coach Steve Fisher said. “To end the season the way we did is extremely difficult.”

The Hoosiers erased deficits of 10 points early in the second half and five points a bit later. Trailing 83-82 with 40 seconds left, Indiana’s Marshall Strickland harassed San Diego State’s Brandon Heath near the halfcourt line and the ball crossed into the backcourt.

Thinking he couldn’t touch it lest he be called for a backcourt violation, Heath tried to shield Strickland from the ball. They both dove after it for a jump ball and Indiana got possession.

“I thought I couldn’t touch it,” Heath said. “If I touch it, it would have been a backcourt violation.”

Strickland claimed he never touched the ball, which would have made it a backcourt violation had Heath touched it first.

Either way, the damage had been done.

After a timeout, the Hoosiers worked it to Vaden — sort of. He snagged a bad pass from Roderick Wilmont that got tipped into the air by Slaughter. Hobbling with a hurting left ankle that almost kept him out of this game, Vaden spotted up about a step behind the line and swished the 3, giving Indiana an 85-83 lead.

“I was open,” Vaden said. “It was like any other shot. I was open and I knocked it down.”

San Diego State’s desperation possession came up empty and Wilmont hit two free throws for the final margin.

Next up for the Hoosiers in the Oakland regional is a second-round game against Gonzaga on Saturday.

Davis said they’ll be ready.

“We’ve been in a situation the last three weeks where if we lose, we are probably out of the Tournament,” Davis said. “That situation has really helped us. We showed a lot of character and kept going and going and going.”

Davis improved to 115-78 over his tumultuous six years at Indiana, which will come to an end whenever this season is over. He announced his resignation four weeks ago — saying his players deserved better than to play for a coach always under fire.

Since then, the Hoosiers have played better, finally living up to the potential they showed when they were ranked in the top 10 early in January.

And Davis claims he’s finally enjoying himself.

Dressed impeccably, as usual, in his four-button suit and red tie, he hardly acted like a coach who wanted it to be over. Stomping, cajoling, peering into the court, he earned his money all the way through.

He watched the Aztecs shoot an amazing 77 percent from 3-point range in the first half. Somehow, Indiana only trailed 44-41.

“To be down by only three when they’re shooting like that, I felt pretty good,” Davis said.

San Diego State outrebounded Indiana 36-31, had one more assist and generally took better shots and made better decisions all night long.

But it wasn’t meant to end for Davis on this night.

Vaden was one of three Hoosiers to finish with 18 points, and maybe the most unlikely to pull it off.

The ankle injury made him a question mark for this game and he was pressing too much at the end — taking a terrible 3 with 7½ minutes left, then making a bad pass with about 90 seconds remaining that could have cost the Hoosiers the game.

He came through when it counted the most — with his coach one miss away from unemployment

“Some people told me that if I didn’t need him, I shouldn’t have played him tonight,” Davis said. “Well, we needed him.”

And now Davis will coach in one more game.