The next stop for Minor, however, is Triple-A. Still, McCann, the Atlanta Braves' five-time All-Star catcher, believes Minor has shown he belongs in the major leagues.
"I think he's getting more comfortable, more confident, more understanding of what he needs to do when he gets strike one," McCann said. "He got so many swings and misses on his changeup."
The Braves have won three straight following a 1-5 stretch.
Toronto manager John Farrell, who called a team meeting before the game to let pitcher Ricky Romero address comments he made in criticizing the offense on Monday, watched his club struggle at the plate for the third straight game.
The Blue Jays have scored two runs in losing three straight on the road for the first time since April 30-May 3. They have dropped eight of 12 overall.
Minor (1-2) allowed five hits, one run, one intentional walk and struck out a season-high eight in seven innings. After so many struggles since last August, Minor took some good advice from teammates who told him to relax during his bullpen session.
"Before the game they were saying have fun, pitch to contact," Minor said. "Don't walk anybody."
Minor, a first-round draft pick in 2009, was optioned to Triple-A Gwinnett after the game with right-hander Brandon Beachy coming off the disabled list and starting Wednesday against Toronto.
The Braves have already called up Minor three times this season. Before Tuesday, the left-hander had gone 0-4 with a 9.07 ERA over his last nine starts.
"It seems like he was still a little timid up until tonight," Jones said. "I told him in spring training, you've got to come out of the bullpen breathing fire. That's how you earn the respect of the everyday players."
Atlanta took a 4-1 lead in the third on McCann's 12th homer and Alex Gonzalez's RBI double off rookie Zach Stewart (0-1), who allowed 10 hits, five runs, three walks and struck out two in 3 2/3 innings.
After Heyward put the Braves ahead 5-1 with an RBI single in the fourth, Stewart intentionally walked McCann to load the bases. Reliever Marc Rzepczynski limited the damage, though, by striking out Freddie Freeman on three pitches.
McCann, who went 2 for 3, is hitting .327 with 10 homers and 22 RBIs since May 17. He has reached base safely in 22 of his last 28 games.
"I've been seeing the ball well all season long," McCann said. "And early in the year, I talked to my brother (Brad McCann) about some adjustments and ever since we've talked I've been able to really let the bat fly through the zone. I'm lucky to have people in my family that understand baseball and understand hitting."
Minor escaped a jam in the fourth after Lind singled and moved to third on Jose Molina's double with one out. But after striking out Rajai Davis and intentionally walking Mike McCoy, Minor held his 4-1 lead with a strikeout of Stewart. He retired the last 10 batters he faced.
Toronto slugger Jose Bautista, who began the game tied for the major-league lead with 21 homers, has gone deep just once in his last 22 games. He went 0 for 4 for the second straight night.
Bautista isn't too concerned about the offense, insisting that nobody is pressing to deliver a clutch hit.
"You run into good pitching, and it happens," Bautista said. "The Braves have done a good job, and the Reds pitched well against us in Cincinnati. It's only been three games. It's nothing major. I don't think anybody's concerned. We've just got to turn the page, come out tomorrow and try to score more runs."
The Blue Jays never gave themselves much of a chance against Minor and two relievers.
"It felt nice to finally get a win this year, but mostly I'm just trying to get a win for the team," Minor said.
He doesn't know how long the Braves will keep him at Gwinnett.
"I understand there's not a spot for me (in the Atlanta rotation)," Minor said. "Guys ahead of me are better than me. I'll just go down there and work on things."
Jones returned to the lineup after missing four games with a right adductor strain and went 1 for 3 with a run scored. ... Rzepczynski has held left-handed hitters to a .172 average (10 for 58) this season. ... Toronto has just one series win against the NL since 2004. ... Stewart, making his second career start, watched his ERA rise from 2.57 to 5.91. ... Atlanta purchased the contract of veteran infielder Julio Lugo before the game and optioned Diory Hernandez to Gwinnett.