But down the stretch, it was time for Paul Pierce to take over.
Pierce, who has scored at least 30 points in 14 of 16 games, shot 15-of-23 to lead five Celtics in double figures. He also had four assists and three steals to help the Celtics win for the third time in four games and end a three-game losing streak against the Nuggets.
"When you got it going, you got it going," said Pierce, who shot 4-of-6 in the fourth quarter. "I just keep my focus down the stretch. That's when I want the ball. I'm just not afraid to fail."
Anthony scored 36 points on 14-of-21 shooting but was held to 10 in the second half and two in the fourth quarter. The Nuggets fell to 8-3 when Anthony scores at least 35 points.
"Carmelo seemed like he was going to have a career night," Pierce said. "But we buckled down and got the stops we needed."
The Nuggets led the entire first half, but there were 13 ties and 17 lead changes in the second half. Pierce gave the Celtics the lead for good on a dunk from the baseline with 2:43 remaining after Kenyon Martin made just 1-of-2 free throws.
"[Pierce] has been making those big shots for us," Celtics forward Ryan Gomes said. "Earlier in the season, other teams were making those shots against us. It's reversing right now."
The Nuggets went the final 4:35 without a field goal and turned the ball over seven times in the fourth.
After Delonte West missed a 3-pointer from the baseline with 1:12 left, Gomes stole Martin's outlet pass. On the ensuing possession, Pierce made a 17-foot fadeaway jumper over Ruben Patterson to extend the Celtics' lead to 104-101.
"What can I say," Patterson said. "I had a hand all in his face. Fadeaway jump shot with a hand in your face, come on, that's a tough shot."
Anthony then missed a layup on the Nuggets' possession, and Pierce iced the game for Boston with a bank shot from just inside the 3-point line.
West, who returned to the lineup after missing three games with a strained right groin, had 12 points and five assists. Gomes added 11 points and 11 rebounds and the Celtics improved to 9-5 with him in the starting lineup.
Anthony made his first 11 shots and scored 26 first-half points to lead the Nuggets to a 58-56 halftime lead.
He didn't miss until his 30-foot heave at the buzzer in the second quarter rimmed out. He then missed his first three attempts of the second half, and the Celtics took advantage.
"They started double- and triple-teaming me, bringing everybody over," Anthony said. "So I had to kick it out, that's how my teammates score. We were doing it pretty good for a little bit, until probably the end of the game."
Boston trailed by as many as 12 in the first half, but went on a 13-4 run spanning both halves to close the gap.
West's layup with 10:42 remaining in the third tied the game at 60. After Patterson made 1-of-2 free throws, Raef LaFrentz made a 3-pointer to give the Celtics their first lead of the game, 63-61.
The Nuggets fell to 2-1 on their seven-game, 10-day road trip.
Andre Miller scored 19 and Patterson added 14 for the Nuggets, who dropped to 5-2 with Patterson in the starting lineup.
The Celtics wore their gold-trimmed St. Patrick's Day uniform for the first time. ... The Celtics are 27-6 all time at home against the Nuggets. ... Martin came off the bench after missing four games with tendinitis in his left knee. He had five points and five rebounds. ... Kendrick Perkins returned to the Celtics' lineup after missing 13 games with a dislocated left shoulder. ... Former Cincinnati coach Bob Huggins is traveling with the Nuggets on their trip. ... The Celtics have never been
swept by the Nuggets in consecutive seasons. ... The Nuggets are 9-17 with Martin and Marcus Camby both in the lineup.