Shabazz Napier had a career-high 34 points for the Huskies (20-5, 8-4 ACC), who won for the sixth time in their last seven games.
Napier notched six points in overtime and Ryan Boatright scored eight of his 21 points in OT.
UConn forced 18 turnovers and outscored Memphis (19-6 8-4) 29-6 at the free throw line.
Joe Jackson had 24 points and seven assists to lead Memphis, whch shot 54.8 percent from the floor.
Geron Johnson scored 15 points and had eight rebounds but fouled out early in overtime.
UConn led 36-35 at halftime and tied the score 69-69 on Napier's free throws with 52 seconds to play to force overtime.