The Red Sox left-hander allowed nine runs on eight hits in 4 2/3 innings, after coming into the game with a 0.44 ERA.
According to Elias Sports Bureau, he was the first pitcher in baseball history to go six or more innings while allowing no more than one run on three hits in his first three starts.
While Rodriguez had pinpoint command during his first three outings, he had a tough time finding the strike zone against Toronto. He threw 88 pitches on Sunday, 45 for strikes, and walked three batters.
"It was a little bit out of control," Rodriguez said. "I just have to throw better pitches.
"You try to make the right pitches, they just got a lot of base hits."
Much of Rodriguez's undoing came from sloppy defense in the fourth and fifth innings. A misplayed ball by right fielder Alejandro De Aza fell in for a single, before second baseman Dustin Pedroia lost a popup in the sun. That exacerbated things when Ryan Goins hit a three-run home run later in the fourth inning to give the Blue Jays a 6-0 lead.
"Early on in the [fourth] inning, they did a good job of putting the bat on the ball, fighting off some tough pitches. They get a break on some balls that fell in and then a big home run," said Red Sox manager John Farrell.
The team's troubles in the fifth began after Rodriguez retired the first two batters. Edwin Encarnacion drew a walk, before four Red Sox players were unable to catch a fly ball in right-center field. That led to a two-run double by Russell Martin that chased Rodriguez.
"I just tried to make good pitches, like you saw. The rest, getting wild a bit, with balls. Stuff like that happens in the game," Rodriguez said. "I just tried to make the right pitches in the situation and just do my job. A lot of base hits, bloopers and ground balls."
Quinn Roberts is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.