KANSAS CITY, Mo. — If anyone says La Salle is making its first trip to the round of 16 in a very, very long time, don't believe it.

The last time the upstart Explorers got this far, the NCAA tournament didn't even have a round of 16.

But now it does and the little school from Philadelphia is there.

Tyrone Garland banked home a scooping layup with two seconds left and the 13th-seeded Explorers beat Mississippi 76-74 on Sunday, making this their deepest run since they advanced to the championship game of the 24-team field in 1955.

"Time was running out, and I felt like I could get the drive," Garland said. "When I cut, I just saw an opening and took the ball up."

By inches, the ball off the hands of the 6-foot-1 Garland cleared the outstretched hands of Reginald Buckner, the Rebels' muscular 6-9 center.

"He blocked my shot a couple times during the game, but I ain't scared of nobody," Garland said. "I went in there and knew if I could get an open shot, I could make it."

In the regional semifinals in Los Angeles on Thursday, the Explorers will meet ninth-seeded Wichita State.

Ramon Galloway had 24 points for the last remaining team in the tournament from the Atlantic 10. The Explorers (24-9) were playing their third game in five days after starting the tournament in the First Four on Wednesday in Dayton, Ohio.

But they showed no fatigue.

"We're pretty young. It just feels like AAU all over again. We play a game, go to sleep, wake up, play another game," said Galloway. "We're pretty excited for the whole trip."

No. 12 Ole Miss (27-9) led 74-72 with 1:58 left but failed to reach the regional semifinals for the first time since 2001.

"I've always said that winning teams make winning plays, and to La Salle's credit, they made the winning plays down the stretch," Ole Miss coach Andy Kennedy said.

The Rebels had a height advantage over La Salle's four-guard lineup and outrebounded the Explorers 40-30 but failed to make their zone defense work.

"We couldn't contain them off the dribble," Kennedy said. "We couldn't contain them even in a zone."

After Tyreek Duren's two foul shots tied it 74-all at the 1:07 mark, Mississippi star and team lightning rod Marshall Henderson missed an off-balance bank shot that would have given the Rebels the lead.

Henderson had 21 points in a game with 11 lead changes.

Duren had 19 points for La Salle and Garland had 17.

Murphy Holloway had 14 points for Mississippi, which fell one win shy of breaking the school record. Jarvis Summers had 12 and Nick Williams had 10 for the Rebels, who were a miserable 10 for 21 from the foul line.

In the frantic final seconds, Mississippi's LaDarius White missed from the top of the key and the ball scooted out of bounds while everybody went for the rebound.

The Rebels were given possession and Henderson's off-balance shot failed to draw iron. Before he could launch another try, the buzzer sounded, giving La Salle possession with 33.2 seconds left even though Henderson pleaded with an official, saying, "He took my hand off."

"I know I was fouled and the ref knows I was fouled but he said he's not calling a foul with 1 second left (on the shot clock)," Henderson said later. "I drove in, got the rebound and when I went up, he took my whole left hand out and I was like, 'That's a foul.'"

On their last possession, the Explorers brought the ball up court, with most everybody expecting Galloway to take the shot. But Garland worked his way inside and threw up his game-winner over Buckner.

"We didn't finish on a strong note, we finished on a low note," Henderson said. "We're going home and it stinks because I know a lot of people that are around are going to pat us on the back and tell us we did a great job but the way I played there at the end I feel that I was totally a disgrace to my teammates and let them down."

Summers missed a desperation heave for Ole Miss.

Galloway, a 6-3 guard and the Explorers' lone senior on the starting five, played the entire 20 minutes of the first half and drilled 5 of 8 3-pointers while scoring 19 points.

La Salle coach John Giannini rejected any suggestion that this victory represents college hoops parity.

"Parity makes it sound like everyone's average," he said. "Everybody's good."