The eighth-seeded Bulls had stunned the Celtics in two games in Boston to seize a 2-0 lead in the best-of-seven series.
But the Celtics, rocked this week by the death of star Isaiah Thomas' sister, Chyna, in a one-car accident, responded as the series shifted to Chicago.
"We wanted to play for him," Boston's Avery Bradley said of the team's response to Thomas' tough week. "We wanted to play hard and tonight I feel like we put another smile on his face."
Celtics coach Brad Stevens said Thomas was "feeling better" after travelling to Washington state to connect with family after playing in the first two games of the series.
"It's been a hard week, he's had his ups and downs," Stevens said. "I think going was a good thing, but it was hard."
The Celtics were also buoyed by a message from former Boston star Kevin Garnett, who told them to "just let go and have fun".
Al Horford scored 18 points and Thomas and Jae Crowder had 16 apiece for the Celtics.
Four Boston starters reached double figures. Bradley scored 15 points and Terry Rozier finished with 11.
Dwyane Wade led Chicago with 18 points and Jimmy Butler, who connected on just seven of his 21 shots from the floor, finished with 14. He didn't go to the free-throw line once.
Robin Lopez finished with 12 points and Nikola Mirotic scored 12 for the Bulls, who struggled offensively without injured point guard Rajon Rondo.
The Bulls announced Friday Rondo was out indefinitely with a broken right thumb.
Rondo, clad in a short-sleeved sports coat that showed a cast on his wrist, sat on the bench and called advice and encouragement to his teammates.
Wade said the Bulls couldn't pin the defeat on Rondon's injury.
"Just like every injury, every blow, it hurts the team in the moment, but we have to move past it," Wade said. "We have to figure out a way with our young point guards and other guys on this roster to just be better next game."
The Celtics led by as many as 20 in the second quarter, but were up only 44-41 at halftime.
The Bulls closed to within a point in the first minute of the second half.
But Boston responded, stretching the lead to double digits with a run that included back-to-back three-pointers from Thomas.
Boston led by 13 after three quarters and by as many as 20 in the fourth.
"It's a game of runs," Horford said. "For us, in the first two games, we didn't handle it well when they went on a run. Tonight, we were more composed and handled it much better."
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