TORONTO -- Rowdy Tellez had only ever done it five times in his professional career before Tuesday night.

The left-handed-hitting slugger sent two balls out of the park at Rogers Centre in the Blue Jays' 10-3 win over the Red Sox, driving in five runs in his first two-homer game at the Major League level and providing some much-needed run support for Toronto starter Marcus Stroman.

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Tellez accomplished the feat on five occasions in the Minors, going yard twice in two Buffalo Bisons games last season, in his first two Triple-A at-bats on April 8, 2017, hitting two dingers on Aug. 7, 2016, for the New Hampshire Fisher Cats, and homering twice on July 3, 2015, with the Class A Advanced Dunedin Blue Jays.

The biggest difference on Tuesday was that both of Tellez's long balls came against southpaw Eduardo Rodriguez. According to Tellez, the last time he might have hit two home runs in a game off a lefty was in high school.

"I'm just glad [manager] Charlie [Montoyo] gives me the opportunity to face [left-handed pitchers], and I'm just trying to take advantage of it," Tellez said. "It just does a lot for my confidence versus lefties when he throws me in the lineup and lets me face them. Good things can happen, so I'm just excited I got that done."

Added Montoyo: "He's part of our future, so I was thinking, 'Why not? Let's give him a chance, see what he can do,' and he's done it. So that's why he keeps getting the chance, because he's swinging against lefties just like right-handers. He looks pretty comfortable, so I felt good putting him in the lineup against lefties. He's been really good."

Among the 74 homers the California native compiled throughout his seven seasons between the Minors and the Majors before the matchup against the Red Sox, 12 had come off left-handers. Tellez had hit one home run off a lefty at the big league level, which happened to also be his first career grand slam, on April 23 against the Giants.

Though a small sample, Tellez's homer-hitting pace in the Majors is almost twice what it was in the Minors, with one every 18.5 plate appearances in the big leagues -- 12 homers over 222 -- and one every 36.16 plate appearances in the Minor Leagues -- 64 over 2314.

"My goal isn't to hit home runs, it's to hit the ball hard," Tellez said. "So I just think that's an outcome of my approach. I don't think that's anything I'm doing. I've always been a streaky home run hitter where I don't hit one for like a month and then I'll hit like eight in two weeks, so hopefully that starts [now]."

Tellez's two home runs on Tuesday came in consecutive innings, with a two-run shot to right field in the fourth to open the scoring, and a three-run blast to center in the fifth. Tellez and Randal Grichuk -- who went back-to-back with the 24-year-old designated hitter in the fourth inning for his eighth homer of the year -- did the bulk of the damage against Rodriguez, who came out of the game after five innings, allowing six runs on six hits.

Stroman finished six innings, and allowed one run -- a solo homer to Mitch Moreland -- on five hits with four strikeouts. He walked six, but worked out of jams whenever he needed to.

"My stuff is exactly where I thought it would be at," Stroman said. "My stuff's nasty right now and there's times when I lose it because almost it's too nasty -- I can't find the zone with my sinker. I know I'm not scared to face anybody at any time and I'm able to bear down and make big pitches in big moments to kind of get me out of big spots, and I was able to do that today."

Entering Stroman's 11th start of the year, the 28-year-old right-hander had received zero runs of support in six of his 10 starts this season. The Blue Jays had also lost eight of those games, scoring a total of 13 runs in those eight losses.

"Feels great," Stroman said of the support on Tuesday. "We swung the bats unbelievable today. Rowdy, huge day. Up and down the lineup, one through nine, I think we put together really complete ABs and were really complete in the box from the start of the game.

"I've told y'all from the beginning, I knew guys would break out at some point. I'm not really worried about the run support. It's a long year. I have a lot of faith in my guys, each and every time out."

Also ahead of Tuesday's affair, Rodriguez had received the most run support of any of the 88 qualifying pitchers in the Majors, with 8.3 per game, while Stroman's 2.2 per game ranked 86th out of those qualifiers.

"For all of us it was good, not just Marcus, to get that," Tellez said. "I noticed we give him the least amount of run support of any starting pitcher in baseball, I think that's true. So I know for us too, as an offense, it's good to go out there and play well behind a good start from one of our top pitchers."