Brooklyn's Stephen Dennis drew a foul with 5 seconds left to play and the game tied at 96-all, but he missed both free throws. Teletovic was there for the offensive rebound and was fouled by Rob Kurz. Teletovic made the first foul shot, then missed the second and Boston called a timeout with 3.6 seconds left.
Boston got two more shots off, but missed both.
Andray Blatche led Brooklyn with 23 points and nine rebounds and Reggie Evans pulled down 10 boards.
The Nets were coming off a 98-88 win over Washington on Monday night in their Brooklyn debut and played without starters Deron Williams, Joe Johnson, Brook Lopez, Kris Humphries and Gerald Wallace.
Paul Pierce scored 29 points, Rajon Rondo had 11 assists and Kevin Garnett blocked three shots for Boston, which scored 10 straight points during a 20-4 run in the third quarter.
Pierce and Garnett sat out the fourth quarter and the Brooklyn reserves made a run on Boston's, taking a 96-95 lead on Tornike Shengalia's three-point play with 41 seconds left.
The Celtics and Nets play a preseason rematch Thursday night in Brooklyn.