David West scored 32 points and Paul made two key steals in the final minute in the Hornets' 99-96 win Sunday night.
"We made some extra-effort plays," West said. "We knew this was going to be a tough game for us, the way New Jersey had been playing. We wanted to come in here and try to steal one. Guys stepped up and made some big plays for us down the stretch defensively."
With the Nets leading by one with a minute remaining, Harris turned the ball over to Paul, who hit a 19-foot jumper to give the Hornets a 95-94 lead.
On the Nets' following possession, Brook Lopez tried to force a pass to Harris that Paul picked off for his second steal in the closing seconds.
"It's an inbounds play we run too," Paul said. "Devin is under the goal and you know he's coming up to the top to get the ball. I tried to deny him and they hit Brook Lopez. Of course, Devin is going to get the ball back, so I reached a hand in there and tried to smack it away."
The Nets turnover turned into a pair of free throws by Rasual Butler with 9.6 seconds left that clinched the win for the Hornets.
"It's frustrating," Harris said. "We had two turnovers late, didn't get good shots at the basket and they got great shots. We played fabulous all game long, the energy was there. The point-guard play has to be better late in the game."
Butler had 22 points for the Hornets, who extended their winning streak to four. Offensively, Paul finished with 14 points and nine assists.
Harris and Vince Carter each had 26 to pace the Nets, winners of their two previous games.
"We let the game slip away," Carter said. "We played a pretty solid basketball game but in the fourth quarter we had some mental lapses."
Harris also had 14 assists while Jarvis Hayes added 13 points.
Paul made two free throws at the end of the third quarter to give the Hornets a 76-75 lead.
New Orleans threatened to break the game open early in the period, jumping out to 58-45 lead when West sank a fade-away jumper. The Nets regrouped as Harris poured in 15 points in the quarter and Carter added 11.
The game remained tight until right to end, with West carrying the offensive load for the Hornets with 14 points in fourth quarter. In contrast, Carter and Harris only had two points each in the last period.
The contest featured a showdown between two of the league's best young point guards. While Harris had the statistical edge this time, Paul and Hornets had the edge where it counted most, sweeping the two-game season series.
The Hornets' inactives were Melvin Ely and Morris Peterson. The Nets did not dress Keyon Dooling (sore right hip), Eduardo Najera (lower right abdominal strain) and Stromile Swift. ... Dooling had recently been an important part of the Nets bench, averaging 13 points in the previous four games. ... Hayes wound up in the third row chasing an out-of-bounds ball midway through the third quarter. He wound up tangled up with the fans amid the collapsing folding chairs and had to be extricated by Carter.