BOSTON — Without Chauncey Billups, maybe the Knicks had a chance Tuesday night.

Without Amar’e Stoudemire in the second half because of back spasms?

All yours Carmelo. Really, all yours — on the 27th anniversary of the first of Bernard King’s first of back-to-back 46-point playoff games.

‘Melo did all he could, scoring 42 while also grabbing 17 boards.

His all, though, couldn’t prevent Celtics 96, Knicks 93 — the second straight game in this now 2-0 series in which the Knicks lost the lead in the final 15 seconds.

Kevin Garnett’s jump-hook with 13.3 seconds left over Jared Jeffries, who’d just given the lead six seconds earlier, produced the winning points before Anthony, forgoing a shot for the lead, fed Jeffries underneath, who turned the ball over trying to feed Bill Walker in the lane.

Yes, it was an odd cast of characters the Knicks had to play minus Billups all night and then Stoudemire, who layed less than 18 minutes and scored only four before exiting.

But if there were any questions why the Knicks got Anthony, he answered them Tuesday in the wake of his 5-for-18 Game 1.

Until he scored his final points with 2:37 to play, he all but carried the Knicks to what would have been a win for the ages.

Instead, like Sunday’s Game 1, they were so close, yet go home with a deficit from which only 6 percent of teams in such a hole have emerged to win a series.

The Knicks also lost Toney Douglas, Billups’ replacement, early to foul trouble and spotted the Celtics a 10-point first-half lead, then wiped it out to lead for the second straight game at the half.

Still, once Stoudemire — who appeared to hurt his back in the first quarter — was declared out, it looked bleak for Mike D’Antoni’s team as it fell behind by 11 late in the third quarter.

But ‘Melo was getting on a roll, eventually scoring the Knicks’ next 13 points to draw the Knicks within 76-74 before assisting on a Ronny Turiaf score that tied the score, then draining a right-wing 13-footer for the lead.

And the battle was joined — with Roger Mason Jr., getting minutes because of Billups’ absence, draining a three at the 6:10 mark for an 84-82 Knicks’ lead after Rajon Rondo (30 points, seven assists) delivered three straight scores in the paint.

‘Melo then got that lead back again at 2:37, delivering his fourth three of the night despite getting bumped by Paul Pierce, running his meter to 42 points.

But then the Celtics finally got serious about playing Carmelo keep-away, doubling him immediately on the catch, and two Pierce free throws followed by a Kevin Garnett dunk off a Pierce feed made it 92-91, Celtics, with 1:14 left.

Following a timeout, though, and a missed Mason layup, Jeffries of all people found himself all alone with a lane to the basket as the Celtics focused on ‘Melo and delivered a layup for a 93-92 lead with 19.3 seconds left.

Straight out of a timeout exchange, however, Garnett backed in on Jeffries and dropped a 5-foot jump-hook to get the lead back.

For good, it turned out.

D’Antoni said that with Douglas in and Billups out, he didn’t plan to change anything offensively, except to push the pace a little faster than Sunday’s game in the 80s.

The Celtics, though, did by getting Rondo out on the break at the outset and he delivered three end-to-end scores, plus two more leaking out early.

And Rondo’s far more aggressive play drew a quick foul on Douglas, who then basically stopped playing defense before picking up his second at the 6:11 mark of the opening quarter.

By the 4:18 mark of the first quarter, Rondo had 14 points and the Knicks had 11, and Boston eventually extended its lead to 10 after Rondo went to the bench.

But the Knicks wiped that out with a 13-1 run straddling the first and second quarters against an inefficient Celtics bench.

At that point, though, Stoudemire already had tweaked his back and he eventually finished the first half 2-for-9 for four points.

Or, three points fewer than scored by Jeffries, who was in the middle of the Knicks’ surge.

He ended the first half with three boards (two offensive) plus a blocked shot, shot 3-for-5 from the floor and finished a plus-seven primarily because he was a defensive pest.

D’Antoni eventually went deep into his bench and ran Mason out to play the point the final 21/2 minutes. He produced a key steal on Rondo that led to two Shawne Williams free throws, which sent the Knicks in at the half with a 45-44 lead.