Izturis exited the game in the top of the third with a strained groin, and pinch-hiter Mitch Nay replaced him.
Justin Smoak's two-run homer in the third pushed the Blue Jays' lead to 4-1.
Carrera's fourth-inning bunt drove home Ryan Goins, and Daric Barton had an RBI double for a 6-1 Blue Jays lead.
Smith, who is battling to claim one of the Rays' three spots in the rotation, allowed six runs on six hits and three walks while striking out three in 3 2/3 innings.
"Can't look at results. Just going off how I feel. I felt good," Smith said.
The Blue Jays' offense stayed busy in the fifth. Smoak added his second home run, a monster blast off Ernesto Frieri that landed on the roof of the Rays' offices in right field. Later in the inning, Goins added a two-run homer, giving the Blue Jays a 9-1 lead. A sacrifice fly by Josh Thole in the sixth brought the score to 10-1.
The Rays managed three runs in the bottom of the seventh with an RBI double by Joey Butler and a two-run double by Tim Beckham. Taylor Motter added one more on a fielding error in the bottom of the eighth to bring the score to 10-5.
Nay's RBI single in the top of the ninth gave the Blue Jays their final run.
Daniel Norris started for the Blue Jays. The left-hander is competing for the fifth spot in the rotation and allowed a sacrifice fly to Evan Longoria in the first and nothing else. He allowed five hits while striking out five in 5 2/3 innings.
"I threw like one curveball that was bad and sticking out in my mind, but I did a lot of good things," Norris said. "They were swinging early, so I kind of started playing towards that. A lot of sinkers down, getting a lot of ground balls. It was a good outing."
Up next: Knuckleballer R.A. Dickey will make his third start of the spring when the Blue Jays visit the Phillies on Saturday afternoon at Bright House Field, live on MLB.TV at 1:05 p.m. ET. Dickey is expected to pitch five or six innings and will be followed by Jeff Francis, Steve Delabar, Wilton Lopez and Kyle Drabek. Left-hander Aaron Loup also is scheduled to pitch on Saturday, but that will happen in a Minor League game.