The shot clock was running down when Nembhard drained a three-pointer to put the Pacers ahead 109-106 with 17.8 seconds left to play.
It was just his second basket of the night, but it turned the tide for good in a physical, back-and-forth battle in which the Pacers surrendered an early 12-point lead and rallied from nine down in the fourth quarter to cut their deficit in the best-of-seven series to 2-1.
After they dropped the first two games in New York, the move to Indianapolis - and the determination to avoid falling into an 0-3 hole - clearly energised the Pacers.
"Everybody knows what it looks like when you go down 3-0," Haliburton said, a nod to the fact that no NBA team has rallied from that deficit to win a playoff series.
"We had to come out play desperate, play hard," added Haliburton, whose Pacers will now try to level the series at home on Sunday.
Haliburton had six of Indiana's 12 three-pointers. Pascal Siakam scored 26 points and Myles Turner added 21 and 10 rebounds for Indiana.
The banged-up Knicks, already missing Julius Randle, Mitchell Robinson and Bojan Bogdanovic, were also without OG Anunoby after he suffered a hamstring strain in game two.
Knicks star Jalen Brunson, who wasn't confirmed to start until after pre-game warm-ups after hurting his right foot on Wednesday, got off to a slow start, but New York briefly pulled ahead in the second quarter - foreshadowing a third-quarter surge that saw them take a 90-85 lead into the final period.
Donte DiVincenzo led the Knicks scoring with 35 points, connecting on seven of 11 from three-point range.
Brunson finished with 26 points and six assists, hitting a game-tying three-pointer with 42.4 seconds left.
It was still knotted at 106-106 when Haliburton found himself double-teamed and passed to Nembhard with just four seconds on the shot clock.
"I probably held the ball a little too long, I should have been more aggressive," Haliburton said. "I put (Nembhard) in kind of a bad situation and he just made an unbelievable shot - big, big shot.
"He really stepped up to the moment when we needed him most."
Friday's other game saw the Minnesota Timberwolves trying to push the defending champion Denver Nuggets to the brink as they hosted game three of their Western Conference semi-final.
Minnesota, who dominated the Nuggets in winning the first two games in Denver, were bolstered by the return of Defensive Player of the Year Rudy Gobert, who missed game two because of the birth of his first child.
