It's the first trip to the playoffs for DeRozan after four seasons of frustration.
"It makes it feel all worth it, honestly," he said. "The hard work, the struggles, the nights going home where you're just frustrated and don't want to turn on sports. It really shows you that if you stick at it and don't give up, not to sound cliched, but it definitely pays off."
The Atlantic Division-leading Raptors last reached the playoffs in 2007-08, losing to Orlando in five games in the first round. This is their sixth playoff berth in 19 seasons.
"This team has worked so hard," Johnson said. "It was a good game tonight and we deserved it."
"The difference in the game was (DeRozan) making the tough shots," Celtics coach Brad Stevens said.
Toronto led 95-86 on back-to-back jump shots by DeRozan with 8:04 remaining, but Chris Johnson scored four points as Boston replied with an 8-0 run, causing the Raptors to call timeout.
Bayless put Boston in front with a jumper, and then followed a layup by Lowry with a 3, giving the Celtics a 99-97 edge with 3:56 left. Bayless went 8 for 13 from the field against his former team.
Olynyk pushed the lead to four with a layup, but Vasquez fed Lowry for a driving layup and then made a pair of free throws to tie it at 101 with 1:14 remaining.
After a Boston timeout, Lowry rebounded Green's missed shot, but Green hustled back to deny DeRozan a layup. Toronto kept the ball, and DeRozan put the Raptors ahead with a fadeaway jumper.
"It was a great shot," Stevens said.
Rondo tied it for the eighth time with a layup, and Toronto called timeout, advancing the ball to midcourt. Lowry couldn't convert a driving layup, but Johnson grabbed the rebound and banked it home to put the Raptors up by two.
Johnson and DeRozan are the longest serving Raptors, so Casey found it fitting that they played such pivotal roles in the outcome.
"They've been through thick and thin, through good times and bad times," Casey said.
Rondo inbounded the ball to Sullinger with three seconds left, but his shot bounced off the backboard as the buzzer sounded, sending the sellout crowd of 19,800 into joyous celebration.
"The energy in the building just erupted," DeRozan said. "It just shows you how much our fans back us. They stick with us though it all. It was definitely cool to get that reaction."
The Raptors started the game in a funk, missing five of their first six shots, but responded by hitting 10 of their next 12. Valanciunas scored 10 points in the first and Ross had nine as Toronto led 32-26 after one.
Lowry appeared to injure his right ankle when he got tangled up with Bradley after missing a 3 with just over three minutes to go in the second. Lowry was helped off the court but managed to walk to the locker room for treatment.
Green scored seven points in the second and Sullinger had six, but Toronto's Tyler Hansbrough scored a layup with less than a second remaining to give the Raptors a 56-53 lead at halftime.
Lowry had his ankle re-taped during the break and started the second half for Toronto, but DeRozan was the star of the third quarter. He scored 12 points as the Raptors took an 85-73 lead into the fourth.
Lowry said afterward that he was "a little sore," but played down the severity of the injury.
"I'm fine," he said. "Good to go."
Green, who was bothered by a stiff neck in Wednesday's loss to Toronto, started for the Celtics. Stevens said Green was feeling "much better." ... Casey said F Patrick Patterson, out since March 7 with a sore right elbow, could return Sunday or Monday. "He's still sore but he's making great progress," Casey said. ... Lowry played in his 499th career game, but failed to reach the 20-point plateau for the first time in eight games. ... At 41-31, Toronto is guaranteed to finish at .500 or better for the sixth time in franchise history. ... The Raptors are 30-2 this season when leading after three quarters, including a 17-0 mark at home.
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TORONTO, CANADA - March 28: Jonas Valanciunas #17 of the Toronto Raptors shoots against the Boston Celtics on...