TORONTO (AP) - With a losing record and an ERA approaching 5.00 at Double-A, Chad Jenkins began to doubt that he'd achieve his major league dream.

He's not doubting any more.

Jenkins earned his first major league win, Kelly Johnson hit a two-run home run and the Toronto Blue Jays beat the Minnesota Twins 4-3 on Tuesday night.

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A first-round draft pick in 2009, Jenkins went 5-9 with a 4.96 ERA in 20 starts at Double-A New Hampshire this year before the Blue Jays promoted him in early August and put him in the bullpen. He made his first start on Sept. 23 at Tampa.

``There were parts of this year where I honestly wasn't sure whether I was going to get here,' Jenkins said. ``Fortunately the Blue Jays gave me a chance and now I'm just trying to run with it.'

Starting for the third time, Jenkins (1-3) allowed two runs and five hits in five-plus innings. The right-hander walked one and struck out two.

Toronto manager John Farrell has been impressed with Jenkins' attitude on the mound.

``He's a guy that's come up and hasn't been intimidated by the environment at the major league level and has been very effective,' Farrell said. ``Even when he was in the bullpen, he's been efficient. He's done a solid job in the time he's been here.'

Twins manager Ron Gardenhire said Jenkins kept his team off balance with late movement on his fastball.

``Nice looking whip on the ball,' Gardenhire said. ``Our hitters talked about some late jump. You can see the ball OK off him but with that late jump, we didn't really square him up too many times.'

Aaron Loup, Steve Delabar and Darren Oliver all worked one inning before Casey Janssen finished for his 22nd save in 25 chances.

Minnesota's fourth straight defeat, combined with Cleveland's victory over the White Sox, ensured that the Twins will finish with the AL's worst record for the second straight year. They went 63-99 in 2011.

Three-time batting champion Joe Mauer went hitless in three at_bats, dropping his average to .320. Detroit's Miguel Cabrera is leading the batting race, hitting .331. Angels rookie Mike Trout is second.

``Unless (Mauer) goes 9 for 9 tomorrow, he might not be able to catch (Cabrera),' Gardenhire said.

Even so, Wednesday's season finale offers Mauer a chance to play his 147th game, a career high. His success this season has brought redemption after he was limited to 82 games because of injuries in 2011, hitting a career-low .287.

``I'm definitely proud of how many games I've played,' Mauer said. ``It's been a battle, but it's been pretty good.'

The Blue Jays opened the scoring in the third when Adeiny Hechavarria led off with a double and came around on a single by Rajai Davis.

Toronto tacked on two more in the fourth. J.P. Arencibia hit a two-out single and Johnson followed with a homer to right-center off Anthony Swarzak, his 16th.

Johnson's shot came one at-bat after he was caught looking in the second for his 159th strikeout of the season, matching Jose Canseco's team record set in 1998.

Toronto used speed on the bases to open a 4-0 lead in the fifth. Anthony Gose drew a one-out walk and was running when Davis grounded to short. Gose went all the way to third as Davis was thrown out, and scored when Yunel Escobar followed with a hit to left.

The Twins cut the deficit in half and chased Jenkins in the sixth. Eduardo Escobar led off with a single and Span swatted a two-run homer to right, his fourth.

Loup came on and gave up a single to Ben Revere. But Mauer struck out, Revere was caught stealing and Chris Parmalee grounded out.

Minnesota made it 4-3 with a run in the seventh off Delabar. Trevor Plouffe led off with a double, moved to third on a groundout and scored on a two-out double by Alexi Casilla.

Starting in place of Samuel Deduno, who left his last outing with an irritated left eye, Swarzak (3-6) gave up four runs and five hits in five innings. He walked three and struck out two.

``I think he got a little bit tired,' Gardenhire said of Swarzak, who had not started since May 25. ``He made pitches and gave us an opportunity.'

Notes: Blue Jays slugger Edwin Encarnacion (sore left shoulder and neck) did not start for the second straight game. ... Revere had three singles but was picked off first base in both the sixth and eighth. ... Twins reliever Luis Perdomo was struck by Davis' comebacker in the eighth but remained in the game. ... Farrell said he expects his coaching staff to return intact next season. ... Minnesota fell to 26-27 in one-run games. ... Twins LHP Scott Diamond (12-8) faces RHP Brandon Morrow (9-7) in Wednesday's season finale. Diamond, who was born in nearby Guelph, Ontario, will be pitching in Toronto for the first time.