Radcliffe came charging from behind to cut the margin during the sprint and was still gaining when the boats crossed the finish line.
In the first and second novice divisions, Radcliffe finished third. The first novice race was the closest.
Princeton won with a time of 7:04.7, followed by Cornell at 7:05.6 and Radcliffe at 7:07.4.
The second novice boat finished well behind the first-place Princeton and second-place Cornell boats.
Princeton has won the annual regatta 12 times. Radcliffe has emerged victorious seven times and Cornell has never won.
The Radcliffe heavyweights next face Dartmouth and Syracuse at Hanover, N.H., next Saturday.
Yesterday, the Radcliffe lightweights went to Camden N.J., to face stiff competition and choppy waters on the Cooper River.
The Radcliffe varsity boat came in fourth of five boats with a time of 8:20.64.
Princeton won the race with a time of 7:54.86, well ahead of second-place Villanova, which finished at 8:05.95. An exhibition squad from Cambridge crossed the line at 8:06.56. Virginia raced to third in 8:19.99, followed by Radcliffe. UMass placed last at 9:06.14.