Los Angeles held a 74-73 lead with 4:11 to play, but did not score again until the game's final seconds.
Lopez scored 26 points in helping Brooklyn end a two-game skid. Prior to those setbacks the Nets had won five in a row.
Joe Johnson contributed a 3-pointer during the key surge and scored 19 points.
The Clippers have lost two in a row on the heels of a six-game winning streak. Los Angeles will conclude a four-game road trip on Saturday in Atlanta.