Rodriguez was pulled after allowing his second homer of the day, a towering leadoff shot by Randal Grichuk leading off the seventh. Bo Bichette also homered for the Blue Jays, who have lost three straight.
Manager Alex Cora said he likes the way has Rodriguez attacked the strike zone and set up the bullpen this season.
“His stuff is that good. He’s evolving into one of the best lefties in the league,” Cora said. “He has a good feel of what he wants to do.”
Toronto ace Hyun Jin Ryu (1-2) lasted five innings, giving up eight hits, four runs and striking out two.
Trailing 4-2 in the eighth, the Blue Jays had a runner on third with two outs, but Bichette struck out.
Toronto had four hits, the first time it has had four or fewer hits in back-to-back games since July 2019.
“We all know they can do better. They’re just not doing it right now,” Blue Jays manager Charlie Montoyo said. “Hitting’s contagious and when you don’t hit, everybody feels the pressure.”
Rodriguez received a warm greeting from the pandemic-limited Fenway crowd of 4,728. It was a small consolation prize for the left-hander, who missed out on scheduled opening day starts each of the past two seasons.
He still appeared to feed off the home fans’ energy, hurling a 95 mph fastball to strike out Bichette looking in the first inning.
Rodriguez cruised through his first three innings, allowing only a walk.
In the fourth, Bichette jumped on a first-pitch cutter and drove it over the Green Monster to put the Blue Jays in front 1-0.
Christian Arroyo and J.D. Martinez singled ahead of Bogaerts’ blast to left-center in the bottom of the inning. Marwin Gonzalez doubled later in the fourth and Bobby Dalbec drove him in with a triple.
Blue Jays: Cavan Biggio started in right field after missing two games a hand issue. … Toronto placed right-hander T.J. Zeuch on the 10-day injured list with right shoulder tendinitis. Infielder Santiago Espinal was recalled from the club’s alternate training site and started at third base.
Red Sox: Left-hander Chris Sale will report to the team’s spring training facility in Fort Myers, Florida, on Sunday to continue his rehabilitation following Tommy John surgery in March of 2020. “It’s just a matter of time of when he gets on the mound. We’ll go from there,” Cora said.