CAMBRIDGE, Mass. -- For centuries, Harvard has boasted of U.S. presidents and Supreme Court justices and too many Nobel Laureates to count. Walking through Harvard Yard, basketball coach Tommy Amaker would be awestruck -- but never overcome -- by the weight of the school's history.

"I'm not sure you can go on this campus and find something that's never been done before," Amaker said Saturday night after the Crimson beat Princeton 79-67 to clinch at least a share of Harvard's first-ever Ivy League title. "I'm thrilled for our school to finally say that we're champions."

Kyle Casey had a season-high 24 points and Brandyn Curry scored 10 with 10 assists to guarantee the Crimson at least a share of the conference title. Harvard would win the championship outright if Penn beats Princeton on Tuesday night; if the Tigers win, they will share the title and meet Harvard in a one-game playoff for the league's automatic berth in the NCAA tournament.

"It's almost a gift to have another game on Tuesday," Princeton coach Sydney Johnson said. "It's just a blessing that we have another game to play."

Harvard (23-5, 12-2 Ivy League) has not appeared in the NCAA tournament since 1946. It was the only Ivy League school that had not won a championship since the conference was formed in 1956-57.

"We've done what we could do," Amaker said. "But for tonight: What a night for Harvard. What a night for the basketball team."

Golden State guard Jeremy Lin, the first Harvard player in the NBA in almost 50 years, flew back to town after the team's practice in Philadelphia so he could be at the game; the Warriors played the Celtics on Friday, and Lin came back to campus to pick up his diploma. Several NBA officials -- as well as former Harvard and Boston Celtics coach Tom "Satch" Sanders -- were also in the sold-out crowd that hung on a back-and-forth game that had 20 lead changes -- 14 of them, and another four ties, in the first four minutes alone.

As Harvard clinched it with perfect free throw shooting down the stretch, the packed student section bounced in its seats and then stormed the court at the final buzzer, bouncing around beneath the banners hung to commemorate the school's basketball achievements.

All of them for the women's team.

Now the men can hang one of their own.

"This was something that's never been done," Casey said. "A lot of people have tried, put a lot of work in. It was for everyone that's been through the program, and everyone that's supported the program."

Dan Mavraides scored 25 points for Princeton (23-6, 11-2), which could win its 26th Ivy title with a victory over Penn. The Tigers last won the conference and reached the NCAA tournament in 2004.

After shaking hands with their opponents, the Princeton players sat on the bench to watch the party on the floor.

"I think it's important to see what's at stake," Johnson said. "I think it's important to see the celebration. You want to be that team."

Oliver McNally scored 15, Keith Wright had 13 and Brandyn Curry scored 10 with 10 assists for Harvard, which won its 17th straight home game.

The Crimson had lost five straight to Princeton, including a 65-61 win on Feb. 4 that set the Tigers up to cruise to the Ivy title. But they lost to lowly Brown two weekends later, giving Harvard another chance at the conference championship; one week after that, the Crimson lost at Yale, and Princeton was in control again.

Should Princeton beat Penn on Tuesday, the Ivies would consider Harvard and Princeton co-champions, but the automatic berth in the NCAA tournament would go to the winner of a one-game playoff, likely at a neutral site on Friday or Saturday. There is also a chance that the Ivies could get an at-large berth, though that's never happened before.

It would be the seventh playoff in Ivy history, and the first since Yale, Penn and Princeton were tied at the end of the 2001-02 regular season -- the only three-way tie in conference history.

"If we take care of business on Tuesday," Mavraides said, "then they have to beat us twice in a row, at a neutral site."

Harvard led 37-36 after the first half when Laurent Rivard was fouled shooting a 3-pointer with 1.1 seconds left on the clock; he made all three free throws. It was Rivard who committed a similar foul just before the half in the game at Princeton, a play that helped the Tigers turn the game around.

Mavraides had 18 points at the break, and Casey had 17.

But Harvard pulled away in the second, taking a 47-42 lead on Casey's thunderous dunk and a foul shot with 16:46 left. Matt Brown hit a 3-pointer with the shot clock expiring to make it 56-47 and it was still a nine-point game, 67-59, with 4:50 left when Curry converted a three-point play off a drive.

Princeton cut the deficit to six points on Mack Darrow's three-point play with 96 seconds left. Curry drove and left it off the rim, but Rivard drew a charging foul on Douglas Davis and Harvard made all six free throw attempts down the stretch to ice it.