Michael Cuddyer also hit his 17th homer for Minnesota, which had lost three straight overall and five consecutive games at home.
"Radke always seems to step up and give us a good start when we need one," Twins manager Ron Gardenhire said.
Minnesota, which trails Chicago by 2½ games in the AL wild-card race, had been outscored 45-3 over its last five home games and managed only one run in the first three games against Toronto.
"We're not panicking here," said Gardenhire, whose team recorded its fifth shutout of the season. "We got deflated a bit coming off a good road trip, but that happens to all teams."
Shaun Marcum (1-2) yielded four runs and eight hits in five innings for Toronto. He struck out two and walked two in his fifth career start.
"We know we can battle back from just about anything after the start we put ourselves in," Cuddyer said. "We don't get too emotionally high or too emotionally low. We just need to go out and play good baseball no matter how many games we've won or lost in a row."
It was the second straight outing that Radke (12-8) has pitched the Twins (68-49) to a key victory. On Aug. 8, the right-hander pitched seven solid innings to give Minnesota a win over division-leading Detroit one day after learning that standout rookie Francisco Liriano may be lost for the season.
Radke, who is battling soreness in his right shoulder, scattered five hits and struck out three Sunday to help the Twins avoid being swept at home in the four-game series.
"I felt good today," Radke said. "We've struggled the past few days, but the guys went out and scored some early runs and played good defense today."
The 33-year-old Radke has won three straight starts and is 3-0 with a 1.64 ERA in August after going 2-3 with an 8.89 ERA in April.
"Radke is a proven winner in this league," Toronto manager John Gibbons said.
Tyner's double to right scored Justin Morneau to give the Twins a 1-0 lead in the second inning and their first lead of the series. The speedy left-fielder finished a home run short of the cycle.
"Every time (Tyner) came up, I said, 'My God, I gotta get this guy out somehow,"' Marcum said.
Cuddyer hit a solo homer to left-center in the third and Tyner tripled in a run in the sixth to make it 4-0.
Morneau finished with two hits and two RBI.
Bengie Molina had two hits for the Blue Jays.
Toronto (63-49) is four games into a 10-game road trip that now takes them to Tampa Bay and Baltimore. The Blue Jays have won six of their last eight and began Sunday seven games back in the AL East and wild-card races.
"It was very important to win three of four," Toronto's Frank Catalanotto said. "We would have liked to finish the sweep and we're a little disappointed because we were in a position to do so.
|Brad Radke allows only five hits and no runs through seven innings for his 12th victory. (AP)|
|Players of the Game|
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|Toronto Blue Jays|
|Reed Johnson, LF||4||0||1||0||0||0||1||.337|
|Frank Catalanotto, DH||4||0||0||0||0||0||1||.309|
|Vernon Wells, CF||4||0||1||0||0||0||1||.320|
|Troy Glaus, 3B||2||0||0||0||0||1||1||.264|
|Eric Hinske, 3B||2||0||0||0||0||0||1||.264|
|Lyle Overbay, 1B||4||0||0||0||0||3||1||.303|
|Alex Rios, RF||3||0||0||0||0||0||0||.312|
|Bengie Molina, C||3||0||2||0||0||0||0||.281|
|Aaron Hill, 2B||2||0||1||0||1||0||1||.297|
|John McDonald, SS||3||0||0||0||0||1||3||.221|
|DP - Hill-McDonald-Overbay, Ryan-McDonald-Overbay|
|PB - Bengie Molina (8)|
|E - Vernon Wells (4, )|
|Toronto Blue Jays|
|Shaun Marcum (L,1-2)||5||8||4||4||2||2||1||5.12|
|HBP - Bartlett (by Shaun Marcum), Redmond (by Shaun Marcum)|
|WP - Dustin McGowan (2)|
|Pitches-Strikes - Shaun Marcum 105-61, Jason Frasor 15-10, Dustin McGowan 21-12, B.J. Ryan 15-12|
|Ground Balls-Fly Balls - Shaun Marcum 5-7, Jason Frasor 2-0, B.J. Ryan 2-0|
|Batters Faced - Shaun Marcum 26, Jason Frasor 3, Dustin McGowan 5, B.J. Ryan 3|
|Luis Castillo, 2B||5||0||0||0||0||0||4||.285|
|Nick Punto, 3B||4||1||2||0||0||1||1||.312|
|Mike Redmond, C||2||1||0||0||1||0||1||.346|
|Michael Cuddyer, RF||3||1||1||1||1||2||2||.261|
|Justin Morneau, 1B||3||1||2||2||0||0||0||.318|
|Torii Hunter, CF||3||0||0||0||1||1||3||.271|
|Jason Kubel, DH||4||1||1||0||0||1||2||.266|
|Jason Tyner, LF||4||0||3||2||0||0||0||.316|
|Jason Bartlett, SS||3||0||1||0||0||0||2||.356|
|2B - Nick Punto (20, Marcum), Justin Morneau (25, Marcum), Jason Tyner (2, Marcum)|
|3B - Jason Tyner (1, Marcum)|
|HR - Michael Cuddyer (17, Marcum)|
|SF - Justin Morneau (9)|
|RBI - Michael Cuddyer (72), Justin Morneau 2 (103), Jason Tyner 2 (9)|
|2-OUT RBI - Michael Cuddyer (37), Jason Tyner (5)|
|SB - Nick Punto (13, 2nd base off Marcum/Molina)|
|Team LOB - 8|
|DP - Castillo-Bartlett-Morneau|
|Brad Radke (W,12-8)||7||5||0||0||1||3||0||4.43|
|Pitches-Strikes - Brad Radke 96-62, Matt Guerrier 16-11, Joe Nathan 12-7|
|Ground Balls-Fly Balls - Brad Radke 4-13, Matt Guerrier 2-0, Joe Nathan 1-1|
|Batters Faced - Brad Radke 26, Matt Guerrier 3, Joe Nathan 3|
|Attendance - 32811|
|Game Time - 2:35|
|Temperature - 69|
|Umpires - Home - Chris Guccione, First Base - Bruce Froemming, Second Base - Ed Rapuano, Third Base - Brian Runge|