BOSTON — The Nets followed their worst outing of the season with their best Tuesday night.

But even if the effort was better, the outcome was the same. Defeat.

The Nets fell 125-124 in overtime to the Celtics before a sellout crowd of 19,156 at TD Garden, losing on a Jayson Tatum midrange winner at the OT buzzer.

Losing a game they appeared to have won.

The Nets had come back to force overtime.

Rookie Mikel Brown Jr. had 13 points in the fourth quarter, including a game-tying 3-pointer with three-tenths of a second left in regulation to force OT.

But he missed a pair of layups late in overtime, including an inadvisable attempt with the shot clock off that gave way to Tatum’s heroics.

Julius Randle — who’d scored a dozen in that fourth-quarter comeback — hit the first two buckets of the extra stanza to give the Nets a 121-117 lead. But he fouled out with 24 points, while Michael Porter Jr. added 27.

But neither could match Tatum, who poured in a game-high 40 points, eight assists, five rebounds and a career-high 18 (on 22 attempts) from the free-throw line.

And the 17-foot winner that sent the Nets to a heartbreaker.

Brooklyn was clinging to a 124-123 edge when Brown missed a driving layup, and center Day’Ron Sharpe was initially whistled for a loose-ball foul with 6.1 seconds to play in overtime.

But after coach Jordi Fernández called a timeout to challenge, the call was reversed to a foul on Luka Garza.

Brown missed another layup attempt, the unnecessary one, and Boston rebounded with 2.3 seconds to go. The Nets shouldn’t have switched on the last play, but did. The mistake cost them, missing Noah Clowney’s size on Tatum.

The Celtics star was too big for Keon Ellis and that made the difference.

Egor Dëmin was forced out of the game in the first half with a right leg contusion.

After appearing to knock legs with Paul George while defending the latter’s drive, Dëmin came up hobbling on Brooklyn’s ensuing possession.

The young Russian checked out with 2:22 left in the half, limped into the locker room and was ruled out for the rest of the night shortly thereafter.

Other than a five-minute shooting barrage in Cleveland, this was the Nets’ best all-around effort of the young season.

The Nets took a 61-56 edge into intermission and spent the second half trying to protect it.

Brooklyn forced 10 turnovers and held the Celtics to 2-of-16 shooting from deep. They were riding shooting luck that was never going to last.

Still clinging to a 77-70 cushion with 6:40 left in the third quarter after a Randle free throw, the Nets went ice-cold. They conceded an 11-2 run over the next 5 ½ minutes, with Tatum’s 3-pointer leaving them in an 81-79 hole.

The Nets surged back ahead, and Randle put them up 109-104 with 3 minutes left. But they couldn’t hold it.

Boston went on a 10-2 run, with Brooklyn’s only points a strong drive by Brown to knot the score at 111-all with 44.9 seconds to play.

But when Tatum found Derrick White for a go-ahead and-one 11 seconds later, the Nets trailed 114-111.

Porter missed a 3-pointer, and even after Brooklyn grabbed the offensive rebound, Randle couldn’t get a clean look and lost the ball. It swung to Chaney Johnson, who had a strong game but missed a potential tying corner 3.

Boston could have iced it at the line at 117-114, but Mitchell Robinson missed two free throws with 3 seconds left in overtime, setting up Brown’s game-tying 3.