NEW YORK -- The Knicks were seemingly seconds away Tuesday night from finally knocking off the defending champion Boston Celtics, who had thoroughly dominated them in three prior meetings this regular season.

Instead, those final 12 seconds of the fourth quarter turned out to be the beginning of a painful 119-117 overtime loss for the Knicks at Madison Square Garden, allowing the Celtics to complete a four-game regular-season sweep of a club they could meet in the postseason's second round.

After wing Josh Hart scored on a layup to push New York ahead by three points, 107-104, with 11.9 seconds left in regulation, Boston coach Joe Mazzulla wisely elected not to call a timeout, creating a more chaotic atmosphere -- one where the defense couldn't get set -- on the ensuing sequence. Celtics star Jayson Tatum dribbled down the floor and shook OG Anunoby for a nasty step-back 3-pointer to knot the score and stun the Garden crowd with 2.9 ticks left.

On the Boston side, Kristaps Porzingis, who had a huge game with 34 points -- including a 30-foot, go-ahead trey in the final minute of overtime -- suggested that he expected the Knicks to foul before Tatum could get up a potential tying shot.

"They could have [fouled]. They took a gamble. They took a gamble, and Jayson hit a big shot," Porzingis said of Tatum, who finished with 32 points, seven boards and five assists.

Anunoby, one of the league's best defenders, said as much. "I should've fouled. I should've known to foul," Anunoby said, acknowledging that it was an obvious mistake in hindsight.

Hart misfired on a 3 during the final play of regulation, and after Porzingis hit the 3 with 40 seconds left in overtime to give the Celtics a 115-112 advantage, Knicks wing Mikal Bridges bobbled a pass out of bounds that practically secured the victory for Boston (59-20).

It was a much better showing from New York (50-29), which had lost all three of its previous games to Boston by double digits. The Knicks changed a handful of things strategically, including shaking up a handful of defensive matchups. Coach Tom Thibodeau elected to start Anunoby on Tatum, Hart on Jaylen Brown and Bridges on Derrick White. And having backup center Mitchell Robinson seemed to make a difference, too, as his ability to play higher up defensively against screen and rolls was a boost, particularly with Porzingis spacing the floor.

While the atmosphere in the arena was lively, with countless celebrities in the New York crowd and a nationally televised audience, the outcome seemed to matter far more to the Knicks, who were led by Karl-Anthony Towns' 34 points and 14 boards.

Brown logged just 22 minutes and didn't reenter the game after subbing out with 2:46 left in the third period. Similarly, Porzingis didn't initially start the overtime period and only subbed in midway through it despite the game hanging in the balance.

Nonetheless, the Knicks -- who will almost certainly face the Celtics in the conference semifinals if both teams win their first-round playoff series -- liked that they were closer to winning this time after losing by 23, 27 and 13 points in the first three outings. But they made clear that Tuesday wasn't enough to feel good about -- not for a 50-win club that doesn't believe in moral victories and that's now 0-9 against the teams with the three best records in the NBA.

"I think it's something we can build off of. There's a lot of positives we can take from this game, and there's some negatives we can take," said New York captain Jalen Brunson, who finished with 27 points and 10 assists in his second game back after missing nearly a month with an ankle injury. "But yeah: It's a little disappointing, knowing that we fought back and had a chance [to win]."

ESPN's Tim Bontemps contributed to this report.