Lamar Odom chipped in with 16 points for the Heat, who took a 3-2 lead in the series after dropping Games 3 and 4 in New Orleans. No team has won on the road in this series.
Miami has won 15 consecutive games at AmericanAirlines Arena, including the final 12 regular season games they played there.
"Both teams knew how important this game was," Odom said. "Both teams were ready to do whatever they had to do to win the game — scratch, cuss,fight, pull, grab, whatever. But we got it done."
New Orleans was led by Baron Davis’ 33 points and seven assists, both game- highs. P.J. Brown added 12 points and 13 rebounds and Jamaal Magloire scored 10 with 10 boards for the Hornets, who led by as many as 11 points in the game.
Game 6 is scheduled for Sunday at New Orleans Arena.
"We’ve got to win," Hornets guard Darrell Armstrong said. "If we don’t, get your golf clubs, get your fishing gear, get ready for summer."
Wade hit just about as clutch a shot as a rookie has seen these playoffs.
With 54 seconds left in the game, he drilled a huge three-pointer as the shot clock expired to give the Heat an 83-80 lead. Caron Butler blocked an Armstrong three-point attempt at the other end, and New Orleans never recovered.
"I was smiling inside, just wanting to get the shot off," Wade said. "I love that the guys would look to me at that time."
Butler’s free throw at the other end gave Miami a four-point advantage, and he added two more to make it 86-80. Steve Smith hit a three-pointer to pull the Hornets within 86-83, but a Jones free throw extended Miami’s lead to four with 14 seconds remaining.
New Orleans was left without a timeout, and Davis and Smith both missed shots before the end.
"We were in control the whole game, and down the stretch we kind of lost our composure," Davis said.
The Heat rebounded from a poor first-half performance to shoot 44 percent from the game. They were 14-of-26 in the second half, and 8-of-12 in the fourth quarter when they outscored New Orleans 29-20.
The Hornets shot just 35 percent in the game, and made only 12 of their 45 attempts in the second half.
Miami trailed for much of the game, but used an 13-2 run over the third and fourth quarters to erase an eight-point deficit and take a 66-63 lead. Wade’s runner in the lane gave the Heat their first lead since the second quarter, and Udonis Haslem capped the surge with a pair of free throws at 9:26 of the fourth.
New Orleans didn’t score its first points of the fourth until 8:24, when Davis’ three-point play tied the game at 66.
The Hornets led by as many as 11 points in the first half, but never really took control. They were up 24-14 at the end of the first quarter after going on a 10-4 spurt to end the period, but Miami used an impressive 13-0 run to lead briefly in the second.
Jones scored 11 of his 13 first half points during the surge which gave the Heat a 35-33 edge with four minutes remaining before the break. Jones hit a pair of threes during the burst.
The teams played close after that, and New Orleans led 46-42 heading into the locker room.
Davis had 20 first half points for the Hornets, who shot 47 percent before the break. Jones led Miami, which shot just 39 percent.
The Hornets made just five of their 18 shots in the third quarter, but they never let Miami get closer than three. The Heat were just 6-of-14 from the floor in the period, and trailed 63-58 heading into the fourth.
New Orleans Hornets 
Miami Heat 
