The Bulls missed a chance to close out Brooklyn at home in the Eastern Conference quarterfinals and will now face a Game 7 Saturday on the Nets' home floor.
Brooklyn led throughout the second half, but Chicago closed within two when Marco Belinelli hit a 3-pointer with 2:19 to go.
Blatche then hit a jumper that banked off the backboard and he added three free throws in the final 32 seconds to preserve the Brooklyn lead.
The Nets survived a missed 3-point attempt by Belinelli with 7.9 seconds to play. Joakim Noah grabbed the offensive rebound for the Bulls, but he stepped out of bounds and suffered a turnover that all but ended the Chicago hopes.
The Nets missed 11 of their 33 free throws, but they forced 16 turnovers and limited the Bulls to 40 percent shooting.
Belinelli scored 22 points, but the Bulls came up with just seven points from their bench.