Now the Bulldogs need to finish off fourth-place Dartmouth in the season finale to clinch the conference championship outright and earn their first NCAA Tournament berth since Harvard grad John F. Kennedy was in the White House.
''Just one more win to go,'' guard Javier Duren said after scoring 22 points and grabbing nine rebounds to help Yale beat the four-time defending conference champions 62-52 and take over the Ivy lead. ''It's great to feel good about this. But it will be better after one more win.''
Yale (22-8, 11-2) would earn its first NCAA bid since 1962 with a victory at Dartmouth on Saturday. Harvard (20-7, 10-3) could still share the title with a victory over seventh-place Brown on Saturday and a Yale loss.
The schools would play a tiebreaker, if necessary, the following weekend for the NCAA berth. The Ivy League is the only conference that awards its automatic bid to the regular-season champion.
''We've seen crazy things happen in this league,'' Harvard coach Tommy Amaker said. ''Obviously, it's in their hands. But we have a game (left). That's all we're focused on, is being ready tomorrow and winning our game.''
Harvard and Yale have one of the longest-running and most passionate rivalries in all of sports, meeting on the last weekend of every football season for the game that has come to be known as The Game.
In the past two academic years, the schools have played eight times with at least a share of the conference title on the line, including a women's volleyball game last fall the night before the football game also determined the Ivy title.
But the basketball teams had never played this late in the season with the conference lead at stake.
''It's just a great feeling,'' Yale coach James Jones said. ''You work hard for something and then you accomplish your goal.
''It feels good to accomplish part of your goal. It's not over. We want to get to the NCAA Tournament, so we have to go out and win tomorrow.''
Steve Moundou-Missi had 21 points and 10 rebounds for Harvard, which was 2 for 17 from 3-point range and shot under 33 percent from the floor overall. Siyani Chambers had 10 points on 1 for 8 shooting - his only basket a 3-pointer that helped Harvard rally from a double-digit lead early in the second half.
The loss could mean the end of Harvard's four-year reign atop the conference, an era that included two first-round victories in the NCAA Tournament. Harvard opened the season at No. 25 in The Associated Press Top 25, but it dropped out with an opening-week loss to Holy Cross, and the Ivy season proved more challenging as well.
Losses to Dartmouth and Cornell left the Crimson tied with their ancient football - and, oh, academic - rival, and set up the final-weekend matchup for the Ivy lead.
The student section at the sold-out Lavietes Pavillion broke into a ''Safety School!'' chant before the opening tip. But Yale's early lead quieted the gym where Harvard has only recently begun to hang banners.
The Bulldogs' 36 percent shooting was good enough for a 22-19 halftime lead after a first period in which Harvard shot 28 percent - going 0 for 8 from 3-point range. Yale opened the second with nine of the first 11 points in a 14-4 run that gave them a double-digit lead, 35-23 with 14:22 to play.
Chambers hit a 3-pointer - Harvard's first of the game after 10 misses - and then followed a steal with a fast-break alley-oop to Moundou-Missi to cut the deficit to seven points. A Moundou-Missi three-point play made it 35-31.
Yale extended the lead to eight points before two baskets by Moundou-Missi and a pair of free throws by Chambers made it a two-point game, 43-41, with just over 5 minutes left. But Duren made a basket, Matt Townsend made one, too, and then Duren hit a 3-pointer to make it 50-43 and end Harvard's last rally.
In all, Duren - who left the game midway through the half after opening a cut on his forehead when he banged heads with Chambers - scored 13 points in the final three minutes, including eight straight free throws.