Dwyane Wade's jumper gave the Heat a one-point lead with 21 seconds left, but Holiday answered with a jumper from the lane. Miami had another chance, but Wade missed a jumper and Josh Richardson missed a tip.
Davis added 17 rebounds, five blocks and five steals as the Pelicans won their fourth straight. The Heat lost their third straight in a battle of teams that began the night clinging to the final playoff spot in their respective conferences.
Holiday finished with 29 points, Ian Clark had 21 and Nikola Mirotic 10.
Goran Dragic led the Heat with 30 points, Hassan Whiteside had 19 points and 16 rebounds, Wade scored 16, Josh Richardson and Tyler Johnson had 15 each and James Johnson 12.
James Johnson started the scoring in overtime with a jumper, but Holiday answered with a basket.
Dragic made a 3-pointer and another jumper, but Davis ' basket and Mirotic's 3-pointer tied the scored again.
James Johnson's basket gave Miami another lead, but Davis' two free throws tied the score. Holiday fed Davis for a dunk and the Pelicans' first lead of overtime with 1:17 left, but James Johnson tied it soon after.
Wade's runner gave the Heat a 121-119 lead with 36 seconds left, but Davis converted a three-point play to give New Orleans a 122-121 lead with 29 seconds left.
Rajon Rondo's driving basket pulled the Pelicans even at 68 in the third quarter before the Heat made a pair of 3-pointers and built a 78-70 lead.
New Orleans closed within 89-84 when Mirotic scored on a tip-in just before the buzzer ending the third quarter.
The Heat built a 99-94 lead in the fourth, but Holiday made four baskets and Davis one as New Orleans took a 104-99 lead with 2:51 left.
Miami battled back, and after a Holiday turnover, Wade made two free throws to tie the score at 106 with 34 seconds left.
Davis made a jump shot to break the tie with 24 seconds remaining. Wade missed a shot, but Dragic scored on a tip-in to tie the score with 14 seconds left.
The Pelicans had a chance to win, but Davis missed a layup and Dragic rebounded with eight tenths of a second left. Both teams possessed the ball in the final second but couldn't get off a shot.
Dragic scored eight points as Miami shot 52.2 percent from the floor and took a 27-22 lead after one quarter.
Clark got hot in the second quarter, making 6 of 7 shots, including 3 of 4 3-pointers, helping New Orleans cut the deficit to 59-57 at halftime.
--Field Level Media
Miami | New Orleans | |
Goran Dragic 30 | Scoring | Anthony Davis 45 |
Goran Dragic 8 | Assists | Jrue Holiday 9 |
Hassan Whiteside 16 | Rebounds | Anthony Davis 17 |
Goran Dragic 4 | Free Throws Made | Anthony Davis 10 |
Josh Richardson 4 | Steals | Anthony Davis 5 |
James Johnson 2 | Blocks | Anthony Davis 5 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Miami | 123 | 46.3 | 6-18 | 17-26 | 26 | 58 | 5 | 12 | 13 |
New Orleans | 124 | 44.4 | 8-31 | 20-24 | 27 | 56 | 13 | 9 | 15 |