Terry's 3-pointer with 1:31 left in the extra frame put the Celtics ahead for good and helped them avoid a four-game sweep in their first-round Eastern Conference series.
Paul Pierce drained four treys en route to 29 points, grabbed eight rebounds and distributed six assists while Jeff Green provided 26 points and six boards as Boston forced a Game 5, set for Wednesday at Madison Square Garden.
Kevin Garnett supplied 13 points, 17 rebounds and six helpers in the win.
Carmelo Anthony went 16-of-20 from the free throw line on his way to 36 points to go along with seven rebounds for the Knicks.
Raymond Felton donated 27 points in the loss.