Vince Carter scored 20 for the Nets, who lost their fourth straight, unable to take advantage of the absence of Hornets starters Tyson Chandler (left ankle) and David West (back spasms).
Stojakovic adjusted his perimeter game to make up for the Hornets' lack of size, sneaking inside to grab double-digit rebounds for the first time all season.
Rasual Butler added 14 points for New Orleans, which has won three straight. Julian Wright had 11 points and James Posey 10.
Bobby Simmons scored 16 points for the Nets and Keyon Dooling added 12, while rookie Ryan Anderson grabbed a career-high 10 rebounds and Jarvis Hayes added 10 points.
New Orleans put the Nets in a deep hole with a 16-2 run that started with Melvin Ely's reverse layup early in the third quarter.
Stojakovic and Posey each added 3-pointers during the spurt and Paul converted a spinning layup as he was grabbed by Carter, though no foul was called.
It was a poor start for the Nets, who started 3-of-12 from the field and turned the ball over five times, including three times on offensive fouls.
Down by 15 in the final period, the Nets made one last charge with a 9-2 run ignited by Dooling's third 3 of the game and capped by Carter's putback, cutting New Orleans' lead to 91-85 with 3:33 left.
After Paul hit a pull-up in the lane, Simmons' third 3 of the game cut it to 93-88 with 2:24 to go. New Jersey missed its next two shots, and Paul hit a running floater as he was fouled with 59 seconds left, giving New Orleans a 96-88 lead. Paul then added a fast-break, one-handed dunk to punctuate his dominant night.
For the Nets, it was the first game since coach Lawrence Frank benched top starters Carter and Devin Harris for the second half of a blowout loss to Boston, the reason being a poor first half in which New Jersey started 1-of-9 from the field.
Early on, it seemed the Nets had gotten the message, moving well on the offensive end to get the ball to open shooters. They shot better than 50 percent for most of the first two periods. Simmons hit two 3s and scored eight points in the opening quarter, then the Nets took a 38-29 lead on Dooling's second 3-pointer of the second quarter.
Paul pulled New Orleans back with eight points in the last six minutes of the half and Wright, who also had eight points in the quarter, scored inside in the final seconds of the quarter to give the Hornets a 47-46 halftime lead.
Notes: The Hornets are 21-1 when leading after three quarters. ... New Orleans has won 11 of its past 13 home games. ... New Jersey (19-23) dropped to 10-9 on the road.
