The postseason top seeds, who were upset by Miami in last year's Eastern Conference finals, avenged that loss in spectacular fashion with a one-sided wire-to-wire rout at the TD Garden.
Jaylen Brown and Derrick White scored 25 points apiece to lead Boston, who barely noticed the absence of the injured Kristaps Porzingis.
The Celtics threw down the gauntlet in the first quarter, racking up a whopping 41 points to open up a commanding 18-point advantage.
They extended that lead to 22 points by half-time, and kept up the pressure in the third quarter to lead 98-66 heading into the final frame.
Boston head coach Joe Mazzulla could afford to rest his frontline players for the fourth with the game effectively won against an injury-hit Miami team missing Jimmy Butler and Jaime Jaquez Jr.
Mazzulla said the Celtics had not been thinking about last year's series loss to Miami.
"I don't really worry about what happened last year," Mazzulla said. "At the end of the day I liked how we approached the series, regardless of who they were playing.
"It had an intentionality to it, had attention to detail, and had a consistent physicality," he added.
"And that's the most important thing, regardless of who we're playing. We wake up tomorrow and we've got to do it all over again versus another team."
Boston will now face either the fourth-seeded Cleveland Cavaliers or fifth seeds Orlando in the Eastern Conference semi-finals. Cleveland lead that series 3-2.
The Celtics advance brimming with confidence after ruthlessly taking care of eighth-seeded Miami in five games.
White's 25-point haul included five three-pointers while Jayson Tatum added 16 points including 12 rebounds with three assists.
Sam Hauser added 17 points off the bench while Jrue Holiday also cracked double figures with 10 points.
Clippers thrashed
In Wednesday's other play-off game, Luka Doncic delivered a 35-point performance as the Dallas Mavericks thrashed the Los Angeles Clippers 123-93 on the road to take a 3-2 series lead.
The 30-point margin of defeat was the Clippers' heaviest-ever NBA play-off loss.
Dallas, who can clinch the series with victory in Game 6 back in Texas on Friday, pulled away towards the end of the first half to open up a 56-46 lead at the break.
They extended that advantage to 20 points after outscoring Los Angeles 33-23 in the third quarter and piled on in the fourth to open up a 32-point advantage at one stage.
Doncic finished with 35 points, 10 assists and seven rebounds, while Maxi Kleber added 15 from the bench. Kyrie Irving had a relatively quiet night with 14 points.
"In the play-offs it doesn't matter if you win by one point or you win by 50 points - but it's still a good win," Doncic said afterwards.
"But the job is not done. We've got one more we need to win. We're gonna get ready for the next game."
The Clippers were left licking their wounds after a humiliating loss that saw their offense make just nine of 35 attempted three-pointers, and 33 of 87 from the field.
Paul George and Ivica Zubac led the scoring with a meagre 15 points each, while James Harden added just seven points and Russell Westbrook six from the bench.
"We didn't play our best game, we understand that collectively. We'll be better for Game 6," Clippers coach Tyronn Lue said.
"Overall we weren't good on both sides of the basketball and just had a bad day."
Asked what he attributed Harden's poor performance to, Lue replied: "Being human. He's allowed to have a bad game."
