Davis also converted a layup as he was fouled on a feed from Gordon, and Gordon's free throw cut the Clippers' lead to 79-77 heading into the fourth quarter.
Yet the Clippers soon were back up by 10 after Eric Bledsoe and Matt Barnes each hit 3s during an 8-0 run that made it 89-79.
"Our bench was amazing," Paul said. "That's very important, because down the stretch (the Hornets) tried to trap and tonight we were able to make them pay when we found Matt in the corner for the dagger."
The Clippers' lead grew to 98-85 after Griffin hit a short running hook and added a free throw with 4:27 left, and New Orleans did not threaten after that.
There were eight ties and 14 lead changes in a close first half in which neither team led by more than eight points. Lopez established himself early for New Orleans with 11 first-half points, mostly inside with a short baseline jumper mixed in.
New Orleans led 37-30 after Brian Roberts hit consecutive 3s. Then Paul, who had a quiet first quarter, started to get more involved.
He set up Billups' 3 for one of his five second-quarter assists and added and jumper and foul shot.
As the half came to a close, the Clippers made four straight 3s — two each by Butler and Billups — including one that Billups banked off the backboard. The shots resulted in a 12-3 run to close the quarter, putting Los Angeles ahead 56-48 at halftime.
NOTES: DeAndre Jordan had 11 rebounds to go with a fast-break alley-oop jam on a lob from Paul. ... The fans in courtside seats included Davis' college coach, Kentucky's John Calipari, as well as actress Lori Loughlin and Saints head coach Sean Payton. ... The Clippers continue their road trip Friday at San Antonio. ... The Hornets continue their home stand Friday against Miami, which saw its 27-game winning streak end Wednesday night in Chicago.