Diamond has now tossed 14 scoreless innings to start the season, while Dozier has provided excellent defense at shortstop and a .267 average in seven games.
"A nice win for us getting two out of four, which is a start," Twins manager Ron Gardenhire said. "Scott Diamond was fantastic. He threw the ball great. Just like his last outing, changed speeds, used his breaking ball and moved the ball in and out, and I think for the most part you saw him ahead in the count and get the ground balls.
"And Dozier is playing great shortstop and getting some big hits. He put one in the seats today. A big smile on his face, which is kind of fun. And he's playing the heck out of shortstop."
Diamond has yet to allow a run in two starts this season, as he followed up seven shutout innings against the Angels on Tuesday with seven scoreless against Toronto.
The Canada native kept the Blue Jays off-balance, allowing just five hits without a walk, while striking out four.
"Diamond threw strikes, he had an assortment of pitches," Blue Jays manager John Farrell said. "Most importantly, though, he threw strikes and got ahead."
His impressive outing came despite getting hit in the back of his left shoulder by a line drive in the second inning. But Diamond said he was fine after the game, and said it didn't affect him while he was on the mound.
"The key was getting back down to throwing strikes," Diamond said. "Me and [catcher Drew] Butera worked well. We knew how we wanted to handle these guys. So we just wanted to keep attacking."
He was backed by Dozier, who made several nice plays in the field and picked up two hits, including his homer in the third inning off left-hander Ricky Romero. It was a towering home run that landed in the second deck.
"I did know it was going," said Dozier, who exchanged two signed balls and batting gloves with a fan for the home run ball. "He left a changeup up in the zone. I was able to get some good wood on it. I didn't even know it went upper deck until [Trevor] Plouffe told me afterward. So that was a lot of fun."
Romero struggled with his control, allowing four runs on nine hits and five walks over 5 1/3 innings.
The Twins broke it open with three runs in the fifth, as they loaded the bases with nobody out after singles from Denard Span and Dozier and a walk from Joe Mauer. Josh Willingham brought home a run with a bases-loaded walk before Ryan Doumit added a two-run single.
"We faced a very good pitcher in Romero over there, and we made him work," Gardenhire said. "Not too many people have done that this year."
Reliever Jared Burton saw his streak of 11 1/3 hitless innings come to an end in the eighth, when Rajai Davis opened the frame with a single up the middle. Davis came around to score on a single from Yunel Escobar before the Blue Jays loaded the bases with one out.
Left-hander Glen Perkins relieved Burton and got pinch-hitter Eric Thames to hit into an RBI groundout on a diving play from Mauer at first base before allowing another run to score on a wild pitch.
But Perkins got Brett Lawrie to ground out to end the inning, and closer Matt Capps tossed a scoreless ninth to pick up his seventh save.
Capps was able to strand a runner at third base, as he got Kelly Johnson to strike out on a 2-2 splitter that stayed up in the zone after throwing a belt-high fastball to stay perfect in save opportunities this season.
"If I threw that last pitch in the first pitch of the at-bat, we're probably not smiling here," Capps said. "So I think the fastball, the pitch before, set it up pretty good."