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.
- Eric Hinske replaced Troy Glaus at third base in the fourth inning. Glaus injured his knee swinging and missing at a Radke fastball.
- Radke has reached double digits in wins in 10 of his 12 seasons with the Twins. The only other Twins pitcher to have won 10 or more games in 10 different seasons is Jim Kaat.
- Marcum was called up for his fourth stint with the Blue Jays this season on July 2. His first three call-ups lasted a total of five days.