Raymond Felton added 16 points for the Knicks, who used a 27-4 run spanning halftime to blow it open and move halfway to their first series victory since the 2000 Eastern Conference semifinals. This is their first 2-0 lead since sweeping Toronto in the first round that year.
"For us, we know what type of team we are," Anthony said. "We know when we really buckle down on the defensive end, it's been hard for teams."
It's been difficult for Boston.
Paul Pierce scored 18 points for the Celtics, who will host Game 3 on Friday in their first home game since the Boston Marathon bombings.
They will have to be much sharper to avoid their first opening-round elimination since 2005, before they became one of the NBA's power teams again.
"We have to figure out the offensive side of the ball and not be so stagnated," Boston's Kevin Garnett said. "Figure out ways to score more often."
Garnett had 12 points and 11 rebounds, but battled foul trouble and spent too much time walking back to the bench with a raucous Madison Square Garden crowd finally experiencing playoff success again hounding him every step of the way.
Plagued by turnovers in Game 1, when they managed eight points in the decisive fourth quarter, the Celtics watched it all fall apart 12 minutes earlier this time. They managed only 23 points after halftime, two fewer than in their 85-78 loss Saturday.
"I thought we attacked them in the first half, but they hung in there," Celtics coach Doc Rivers said. "They didn't let us throw a knockout punch, and I thought in the second half they turned that on us and they threw a knockout punch. Several."
Anthony followed his 36-point opener by making 8 of 13 shots in the second half to finish 11 of 24 for the game.
He had said the Knicks needed to treat the game as a "must-win," aware of the difficulty of winning in Boston on Friday with the emotional boost the Celtics will get from finally being home.
They showed that mentality after halftime, outscoring Boston 32-11 in the third quarter.
"I think guys know what's at stake. We don't have to talk about it," veteran forward Kenyon Martin said. "Guys know what it's about right now, and it's about winning a championship."
Iman Shumpert drilled two 3-pointers to open the third and tie it before Pierce scored to give Boston its last lead at 50-48. The Knicks scored 18 of the next 20 points, with the Celtics getting just two free throws from Jeff Green over the next 5-plus minutes. Anthony's jumper with 4:25 remaining in the third capped the run before Garnett finally gave Boston its second basket of the quarter 10 seconds later
The Celtics missed 10 of their first 11 shots of the third while getting outscored 24-4 to open the period.
"I thought in that third quarter we were as good as we've been all year in terms of ball movement and pushing it and making shots," Knicks coach Mike Woodson said.
The Celtics vowed to get Garnett more involved after he shot 4 of 12 while scoring eight points in the opener. But that plan was quickly wrecked when he picked up two fouls in the first 3 minutes, 20 seconds. The Celtics shook it off and led 20-15 when Jason Terry made a 3-pointer with 1:57 left for his first basket of the series.
But the Knicks scored 11 straight to end the period.
Knicks 87, Celtics 71
R Carmelo Anthony scores 34 points and J.R. Smith puts up 19 as New York routs Boston.