The teams were tied at 73 after three periods, and Memphis entered the game 1-39 when tied or trailing entering the final quarter.
Mike Miller scored 22 for Memphis, and Darko Milicic added 16 points and grabbed 11 rebounds. Kyle Lowry finished with 15 points, and hit all four of his free throws in the final 28 seconds to help Memphis maintain the lead.
Richard Jefferson led the Nets with 22 points, and Devin Harris, starting his second game since coming to New Jersey in a trade with Dallas for Jason Kidd, scored 20 points and had eight assists. Nenad Krstic scored 16 points and had nine rebounds.
Memphis, which trailed by 10 in the second half, was able to take a lead in the fourth quarter as Warrick scored seven points in the first three minutes.
The Grizzlies maintained the advantage the rest of the way, sending the Nets to their third straight loss.
It was Miller's first game back after missing seven games with a sore back, and the Grizzlies' second-leading scorer came out shooting, connecting on 9-for-13.
It was tied at 53 at halftime as Jefferson had 16 points and Krstic added 10 for New Jersey.
Miller led Memphis scorers with 13 points and Milicic had 12, as the two were a combined 12-of-15 shooting in the half.
New Jersey built a 10-point lead on Krstic's jumper to cap a 15-5 rally opening the second half.
But unlike many previous games in the Grizzlies' losing streak, Memphis whittled away at the Nets lead, eventually pulling even at 71. The Nets closed the quarter missing eight of their last nine shots and committing five turnovers.
