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Jordan Farmar's two free throws with 3.8 seconds left helped seal it for the Nets, who snapped a four-game losing streak and improved to 5-29 in road games.
Humphries, Brook Lopez, and Sasha Vujacic scored 18 apiece for New Jersey.
Ramon Sessions scored 21 and J.J. Hickson had 17 with 17 boards for the Cavs, who have lost four straight and seven in a row at home.
In the final 1:09 of OT, Humphries blocked a potential go-ahead layup by Daniel Gibson, grabbed rebound No. 23, made two free throws and stole the ball from Sessions with 28.4 seconds left and the Nets clinging to a 92-90 lead.
Farmar made two free throws before Sessions scored on a layup to make it 94-92. The Cavs were forced to foul and Anthony Morrow's two foul shots put the Nets ahead 96-92 with 11.3 seconds left. Hickson's bucket got the Cavs within two but Farmar dropped his free throws.
It was a rough shooting night for both squads. New Jersey shot just 34 percent, and Cleveland wasn't much better at 37 percent.The Nets were without injured Deron Williams (right wrist) and the Cavs were missing Baron Davis (back spasms).41.50436 -81.69046
New Jersey's Kris Humphries grabbed a career-high 23 rebounds.