Seven strong innings from Price, a setup inning from Koji Uehara and a powerful close by Kimbrel throwing 99 mph.
"I hadn't thrown the ball the way that I know that I can the first two starts," Price said after working seven strong innings to continue his domination over one of his old teams and lead the Red Sox to a 4-2 victory over the Blue Jays in the second game of a four-game series on Saturday.
"To throw the baseball the way I did today against the Blue Jays, which is an extremely good hitting team, feels good."
Xander Bogaerts' three-run homer highlighted a four-run second inning that staked Price to a 4-1 lead.
The left-hander, who signed a seven-year, $217 million contract to leave Toronto for Boston, gave up two runs on six hits, walked none and struck out nine -- capping his day by fanning the side in the seventh.
He didn't want to leave the game, but Uehara took care of the eighth and Kimbrel, whose home-opener disaster is already a distant memory, blew away the middle of the Toronto order while reaching 99 mph in the ninth. He has saved all three games of a three-game winning streak that has lifted the Red Sox to 6-4.
"I don't know if there's a guy in the league that can do it against those three guys," said manager John Farrell. "He's a unique animal."
Price, who has a seven-game winning streak dating back to last season, is 17-2 with a 2.42 ERA lifetime against the Blue Jays. This was his first home win for his new team.
He has thrown a quality start in each of his 13 career home starts against the Jays, a team he helped into the 2015 postseason after being acquired by Toronto from Detroit.
Price (2-0) gave up a first-inning run on a Josh Donaldson triple and Bautista's double and then, after the Red Sox scored four runs in the third, Bautista singled and scored on Encarnacion's double in the fourth.
Marco Estrada (1-1) worked the first six innings and took the loss for the Blue Jays (5-7), who have struck out 12 times in each of the first two games of the series and 124 times in 12 games.
Bogaerts hit his first homer of the season and his first in 24 games dating to last season after third-inning infield hits by Jackie Bradley Jr. and Dustin Pedroia. Later in the inning, Hanley Ramirez doubled and scored on Travis Shaw's single.
"I was feeling good today," Estrada said. "I thought I was going to finish pretty strong. Just one inning got away from me."
It got away after Bradley's comebacker hit him on the calf.
"I got hit and my calf kind of tightened up on me, couldn't really finish pitches," he said. "Felt like I was kind of running forward, trying to land or whatever, but other than that thought I threw the ball well. Calf is still pretty tight but felt better I guess as the game went on, was able to deal with it a little more. But it was too little too late."
Encarnacion, who hit his first two homers of the season on Friday night, has four of Toronto nine hits and has driven in four of its five runs in the first two games of the series.
NOTES: Blue Jays manager John Gibbons credited a member of the media for his decision to wave both hands, two fingers up in the air, and "be like (Richard) Nixon" when he summoned switch-pitcher Pat Venditte from the bullpen on Friday night. Gibbons said WFAN New York Yankees reporter Sweeny Murti made the suggestion when the Yankees were in Toronto earlier this week. ... Two pitchers who have worked in hard luck so far this season square off in the third game of the four-game series on Sunday. Toronto RH Aaron Sanchez is 0-0 with a 1.38 ERA in two starts -- the Jays losing both games 3-2 -- while RH Steven Wright, who allowed two runs in 6 2/3 innings against the Jays in Toronto last Sunday, suffered 3-2 loss in that game. ... Robert Redford was at the game, seated next to the Red Sox dugout for the first 4 1/2 innings on a chilly day.