The Celtics led by 19 points starting the fourth quarter but the Cavaliers fought back with a 21-7 run to climb within 94-88 with 5 minutes remaining.
Cleveland's Jarrett Jack nailed a pair of 3-pointers with 2 1/2 minutes left, narrowing the gap to 98-94, and Dion Walters scored four straight points in the closing seconds to make it 102-100.
Bass then blocked Waiters' drive to the basket and Avery Bradley was fouled with 1 second to go, sealing the Celtics' win.
Bradley finished with 18 points and Bass added 15.
Kyrie Irving poured in 32 points for the Cavaliers, losers of four straight.
Cleveland played without center Andrew Bynum, who the team said has been suspended indefinitely for unspecified conduct detrimental to the team.