Stojakovic hit five of his 3-pointers during a four-minute span in the third quarter as New Orleans turned a single-point deficit into a 19-point lead.
New Orleans made 14 3s as a team, 12 in the second half, giving Los Angeles little hope of staging a comeback.
Jannero Pargo, who led the Hornets with 24 points in a victory over Portland two nights earlier, hit a pair of 3s and finished with 14 points. Rasual Butler hit four 3-pointers for all of his 12 points.
David West had 14 points and 11 rebounds, while Tyson Chandler had 11 points and 13 rebounds. Chris Paul added 14 assists for New Orleans (30-12), which had won 15 of 17.
Corey Maggette led Los Angeles with 24 points, while Cuttino Mobley added 20 and Sam Cassell 16. Chris Kaman had 14 rebounds for the Clippers (13-26), who have lost two of three.
The Clippers appeared primed to stage an upset when Maggette opened the second half with a 3-pointer and a three-point play on a layup as he was fouled. Maggette later added a fast-break layup during a 16-2 run that gave Los Angeles a 53-52 lead.
Hornets coach Byron Scott called time-out and New Orleans returned firing away from long range. It led to a 22-2 run during a 4:07 span, highlighted by Stojakovic's 3-pointers and another 3 by Pargo, which stirred the crowd into a sustained standing applause.
Mobley briefly halted the Hornets' momentum with a pair of 3s during an 8-0 run by the Clippers. The Hornets responded with a 7-0 run of their own, highlighted by Chandler's putback and another tip-in as he was fouled, giving New Orleans an 81-63 lead heading into the final quarter.
