Rhode Island (14-5, 6-2 Atlantic 10) quickly pushed the ball up to Matthews after Mandell Thomas made two free throws to give Fordham (5-13, 0-7) a one-point lead with 9 seconds left.
Matthews drove hard into contact and his first attempt just grazed the rim. He fought to control the rebound but lost balance and, as he fell down backward, tossed the ball up off target. Biruta grabbed the errant shot out of the air and redirected it in for the winning shot.
Biruta finished with 10 points and nine rebounds. Jared Terrell led URI with 18 points.
Eric Paschall had 19 points, Jon Severe scored 17 and Ryan Rhoomes had 10 points and 16 rebounds for Fordham.