Mangano grabbed 12 rebounds for his 10th double-double of the season.
Yale (15-5, 5-1 Ivy League) led by 13 points early in the second half but Princeton cut the deficit to 50-47 after a jumper by Ian Hummer with 2:41 remaining. Mangano's 3-pointer 11 seconds later was the last field goal the Bulldogs would need.
The Bulldogs, who were 15 of 21 from the free throw line, made 5 of 8 in the final 29 seconds to preserve the win.
Neither team shot well from the field as Yale made 35.1 percent (20 of 57) of its field goal attempts while Princeton hit 33.3 percent (19 of 57).
Yale has won three in a row, holding each opponent to 54 points or less.
Hummer had 18 points for the Tigers (11-10, 2-3).
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.
The Central Intercollegiate Athletic Association says it won't move its headquarters, its basketball tournament or other conference championships from North Carolina, despite