NEW YORK — Kevin Durant, quite predictably, came out firing, trying to make up for lost time, and even though he delivered a big number, it still wasn’t enough.

The Celtics swept their first round series against Brooklyn with a 116-112 win, sealed by Al Horford’s put-back with 13 seconds left, despite a 39-point performance by the Nets star.

Jayson Tatum scored 29 points before fouling out, leaving Horford, Jaylen Brown (22 points) and Marcus Smart (20 points, 11 assists) to finish off one of the toughest road wins of the year.

Brown’s three-point play, followed by Marcus Smart’s tip-in of a Grant Williams miss, gave the Celtics a 107-99 lead with 4:38 left.

Durant immediately hit a turnaround over Brown, Irving came back with a drive, and Smart pushed the lead back to 109-103 with an off-balance drive.

Tatum, trying to get position at the top of the circle against Durant, fouled out with 2:49 left and the Celtics leading by six. Irving hit an up-top trey with 2:31 left.

Horford and Irving swapped misses, and when Brown lost the ball dribbling into a crowd, picking up a foul along the way, Durant cut the score to a point (109-108) with a floater.

But this time Brown scored off the baseline with 1:02 left. Durant then missed, but Brown missed a jumper and. with 22.2 seconds left, Smart fouled Durant in the backcourt.

Durant hit his first and missed the second. Smart drove the floor and missed, but Horford finished off the second chance with 13 seconds left for a 113-109 lead.

Seth Curry’s 3-pointer cut the Celtics lead to 90-78 to close out the third quarter, but the Celtics, who led by as many as 15 points, were slowly wearing down their opponent.

Curry also scored the first four points of the fourth, followed by a tough Durant 18-footer over Grant Williams, cutting the Celtics lead to 90-84. Tatum dunked off the break, Irving squeezed off a layup, and Tatum came back again, this time from downtown for a 95-86 edge.

Durant buried a 10-footer, Tatum charged into Blake Griffin for his fifth foul –the Celtics lost the challenge — and Durant got the same call for leaning his shoulder into Marcus Smart’s jaw.

Brown found an open Horford for a 3-pointer, which Curry matched down the other end. Smart and Goran Dragic exchanged 3’s, and Dragic followed up a Derrick White miss with a transition hoop that cut the Celtics lead to 101-96.

Dragic’s 3-pointer with 5:23 left cut the margin to 102-99, answered by a Brown three-point play, followed by Smart’s tip-in of a Grant Williams miss.