Irving added seven assists. It was his eighth game this season with 30 or more points. Jaylen Brown finished with 26 points and five rebounds. The Celtics improved to 13-2 at home this season.
"We had to be resilient practically the whole night, and kind of weather their storms," Irving said. "They kept coming and kept coming. We had to outscore them at some point."
The 124 points was a season-high for Boston. The Celtics shot a season-high 60 percent from the field.
There were eight ties and six lead changes, but Boston never surrendered the lead in the second half.
"That was the only way we were going to win tonight -- the way we were guarding and rebounding," coach Brad Stevens said. "Our guys distributed it well. We did cut and space well. I thought we played with good purpose and authority on offense."
Gary Harris led the Nuggets with a career-high 36 points and six assists. Jamal Murray added 28 points and 10 assists.
The Nuggets went on a 13-2 run to tie the game at 85 in the third quarter. Boston responded in the fourth, using a 9-0 run to open a 106-94 lead.
Denver's Nikola Jokic sat out his seventh straight game with a left ankle sprain.
Celtics forward Al Horford had the night off to rest a right knee bruise.
Nuggets: Will Barton sat out with a lower back bruise. ... Denver connected on their first seven field goal attempts.
Celtics: Shane Larkin had 14 points off the bench. ... Denver's 118 points was an opponent season-high. ... Boston has made 10 or more 3-pointers in 11 straight games. ... Marcus Morris sat out for the fourth time in five games rehabbing his left knee.
"We came out short-handed -- back-to-back, but that's not an excuse -- and had great energy. That's all you can ask. It's been a long road trip and now we can go back and defend home court." -- Harris.