TORONTO -- Run support has flowed freely for Eduardo Rodriguez in 2019, but that script flipped on Tuesday night at Rogers Centre, as the Red Sox starter was hit hard in the middle innings with little to show from the lineup behind him.

Rodriguez matched the Blue Jays' Marcus Stroman stride for stride in the early innings, with both starters carrying shutouts into the fourth, but that's when Toronto's bats finally got to the left-hander for a series of big blows leading to a 10-3 Boston loss.

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Rowdy Tellez got it started with a two-run shot to right field that thumped off the facing of a video board on the third deck, knocking out some of its lights. Two pitches later, Randal Grichuk turned on one and ripped a low liner over the wall in left field with an exit velocity of 106.8 mph.

"He was very dominant against lefties last year," Red Sox manager Alex Cora said regarding Rodriguez's performance against Tellez. "We were using him in the playoffs like that to get lefties out. It hasn't happened this year, so we'll take a look."

Each of the fourth-inning home runs came against Rodriguez's changeup. Only one of the four home runs he'd allowed entering play on Tuesday had come against that pitch, but neither Tellez nor Grichuk were fooled. Their home runs were the first allowed by Rodriguez in more than a month, dating back to his April 19 start in St. Petersburg against the Rays.

Rodriguez still hadn't see the last of Tellez, though. Toronto's big designated hitter launched his second home run of the night in the very next inning, a three-run shot to put the Blue Jays up 6-0.

"It's frustrating when you know you, with a lefty, you've got to get outs," Rodriguez said. "That's your work. That's your job, lefty on lefty. It's something that I've got to get in the bullpen, work on it and fix it."

There wasn't a great deal of hard contact against Rodriguez outside of the home runs, but those were more than enough to decide the outcome of the game. Rodriguez threw 95 pitches, 57 for strikes, and while his control wasn't necessarily wild, he often found himself working deep into counts or falling behind. Cora suggested that the club and Rodriguez will look to strike a better combination of pitch selection and execution going forward.

"We'll take a look and see where he's at and try to use his stuff in certain spots so he can start doing that," Cora said.

Rodriguez's loss breaks a streak where the Red Sox were 7-0 over his last seven starts and he owned a 4-0 record in decisions.

Missed opportunity in the seventh

Boston's last crack at a comeback came in the seventh inning, when they had finally chased Stroman from the game and loaded the bases with no outs.

The Red Sox had the right man at the plate in Mookie Betts, but lefty reliever Tim Mayza struck Betts out swinging at a high fastball and then struck out Mitch Moreland, who went deep in the sixth, swinging at a slider that dropped below his bat and disappeared as it crossed the plate.

Xander Bogaerts grounded out to end the inning, marking a surprisingly quiet night for the Red Sox bats on the heels of Monday's 12-2 win in which Boston recorded 21 of the 23 hardest-hit balls in play.

Rafael Devers launched a 432-foot solo shot in the eighth to tack on Boston's second run, giving him home runs in back-to-back games. Jackie Bradley Jr. then did the same, sending a ball just over the wall in left field as he continues to show signs of breaking out of his slow start to 2019.

Disagreement between Chavis, Stroman

In the fourth inning, Stroman and the Red Sox's dugout exchanged words in what Stroman later defined as a disagreement between he and Michael Chavis. Cora believes the issue that started it was Stroman pitching quickly after Chavis stepped into the box following a called timeout.

"I was telling [home-plate umpire] Alan [Porter], if he's going to get on our guys, get on him," Cora said. "It's the same thing with him every day. He competes a certain way and people don't like it. It seems like whenever a team comes in, somebody screams at him. I don't know, that's the way he acts. He's a good pitcher. He gets motivated in different ways. Some people like it, some people don't, so whatever. It is what it is."