It was the third straight game with 20 or more points for Rice, who scored 25 and 29 previously.
The Eagles (9-4), who held a 32-24 halftime edge, nearly blew a big lead for the third consecutive game before pulling away in the final 12 minutes.
BC's leading scorer Jared Dudley, averaging 18.8 points, missed his third straight game with a left foot injury.
Eric Flato led the Bulldogs (3-9) with 11 points.
BC had opened a 28-13 first-half advantage before the Bulldogs rallied early in the second half, cutting it to 38-35 with 15 1/2 minutes to play.
Rice and Marshall then combined for all of the points as BC scored 11 of the next 14 and pushed its lead to 49-38 with 11:55 to play. Marshall had six during the run.
Yale never moved closer than eight points the rest of the game.
BC blew an 18-point lead Sunday against Northeastern before pulling away late for the win.
In the previous game, an overtime loss to Duquesne, the Eagles squandered a 10-point lead in the closing 4:43.
Oklahoma State basketball player Tyrek Coger died after a 40-minute team workout on the football stadium stairs in hot weather, university officials said Friday.
Prospective NCAA championship host cities must identify local anti-discrimination laws in a questionnaire being sent out by the college sports governing body.
The Class of 2017 is full of talented big men, but Richards is getting noticed by more programs during the current evaluation period in Las Vegas.