Bautista offered some words of encouragement for the backup outfielder and told him to be aggressive at the plate.
It proved to be sage advice.
Pillar hit a one-out flare to right field off Casey Fien that drove in pinch-runner Erik Kratz with the winning run to give the Blue Jays a 5-4 walkoff victory at Rogers Centre.
"It was a slider off the plate and I was just able to nestle it in somewhere," Pillar said. "And it feels good."
Earlier in the inning, Pillar made a miscue in left field by diving for Kurt Suzuki's sinking liner. He couldn't come up with the ball and it rolled by him, allowing the Twins to move within a run.
Eduardo Escobar followed with a blooper off closer Casey Janssen that landed just inside the left-field line and brought Suzuki home with the tying run.
"Baseball is a weird game," Pillar said. "You get a chance to make up for a mistake that you made maybe in the previous inning or early in the game. I was fortunate enough to make that happen."
Edwin Encarnacion had staked Toronto (39-26) to an early lead with a three-run homer in the first inning off Minnesota starter Ricky Nolasco. Jose Reyes added a solo homer in the fifth inning for the Blue Jays, who lead the major leagues with 91 home runs.
With the win, the Blue Jays remained 5 1/2 games ahead of second-place Baltimore in the American League East division standings. The Orioles defeated the Boston Red Sox 4-0 Monday.
It was Toronto's 16th victory in its last 20 games.
"We've been playing good baseball but you still need to win some of those games like that," said Blue Jays manager John Gibbons. "For the longest time, everything has been going our way. Tonight things didn't go our way but we still managed to come out and pull out a nice win."
Minnesota (29-33) scored a pair of quick runs off Toronto starter R.A. Dickey before many fans had taken their seats on a glorious spring evening. Danny Santana hit his first career leadoff home run and Brian Dozier followed with a rainbow shot just inside the foul pole in left field.
Dickey settled down after that, retiring 11 straight batters at one point before Josh Willingham's triple in the sixth inning. The Twins loaded the bases but Dustin McGowan came on and got Trevor Plouffe to ground into a double play to end the threat.
Janssen (1-0), who blew his second save of the season, gave up three hits in the ninth inning. With the crowd deflated after the Twins tied the game, Minnesota pitcher Matt Guerrier (0-1) walked Dioner Navarro to open the bottom of the ninth.
Kratz came in to pinch-run, moved to second on a Reyes single and then scored with room to spare.
"You walk the leadoff guy, you give yourself pretty much a mess and anything can happen after that," said Twins manager Ron Gardenhire.
Pillar, who entered the game in the ninth as a defensive replacement for Melky Cabrera, said his defensive miscue was on his mind when he came to the plate. Thinking about his chat with Bautista, Pillar swung and missed the first two times before making contact.
"It's a huge roller-coaster of emotions right there," he said. "I guess that's baseball. There's a lot of ups and downs. You have to find a way to get back centred and deal with the task at hand."
Notes: Encarnacion leads the Blue Jays with 20 homers this season. Reyes now has four homers this year. Dozier has 13 home runs while Santana has gone deep twice. ... Dickey allowed five hits, two earned runs, two walks and had three strikeouts over 5 1/3 innings. ... Nolasco allowed seven hits, four earned runs and a pair of walks. He had six strikeouts. ... Morales signed a one-year, prorated contract Sunday. The Cuban slugger hit .277 with 23 homers and 80 RBIs with Seattle last season. ... The Twins have hit four leadoff home runs this season. ... Toronto southpaw J.A. Happ is scheduled to start Tuesday night against right-hander Kevin Correia. ... The teams will wrap up the series Wednesday with an early afternoon game. ... Bautista has reached base safely in 62 of 65 games this season. ... Announced attendance was 19,428. The game took two hours 53 minutes to play.
Follow @GregoryStrongCP on Twitter.