Anthony Parker's 3-pointer at the buzzer bounced off the front of the rim and the Cavs fell to the Celtics after trailing by 16 in the first quarter.
Kyrie Irving had 24 points and made all three of his 3-point attempts, but Boston's Kevin Garnett picked him up on the Cavs' final possession, which began off an inbounds pass from Parker with 2.4 seconds left.
With Irving covered, Parker inbounded to Gibson and got the ball back right away. He had a good look from about 2 feet behind the 3-point line, but left it just short. It was Parker's first game back after missing a month with a strained lower back.
Ray Allen had 22 points for the Celtics, including a pair of free throws with 2.4 seconds left. Garnett had 18 points and eight rebounds and Rajon Rondo was held scoreless with 11 assists and six turnovers.
Tristan Thompson had 13 points and 10 rebounds off the bench. Irving and Ramon Sessions outscored the Celtics' point guards, 37-6.