The Blue Jays took two of three from the Rays to win a road series for the first time this season (1-4-1). It also was just the fifth time in 31 tries since 2007 that Toronto won a series at Tropicana Field (5-23-3).
Biagini allowed an unearned run, two hits and struck out four over four innings in his first major league start. The right-hander was inserted into the Toronto rotation after 74 career relief appearances due to injuries to Aaron Sanchez and J.A. Happ, and Mat Latos being designated for assignment.
"The goal for me was always to start in the major leagues," Biagini said. "To say that I did that is pretty cool."
Toronto manager John Gibbons said Biagini will remain in the rotation.
Toronto's bullpen hasn't allowed an earned run in its last 13 1/3 innings.
"Bullpens go in cycles just like everything else, but our guys are starting to step up and establish themselves," Gibbons said.
Barney put the Blue Jays up 2-1 with his first homer of the year. He connected off Alex Cobb (2-3), who gave up two runs and four hits in eight innings.
"I thought Cobb was phenomenal," Rays manager Kevin Cash said. "You saw two polar opposites, with a guy that was buzzing through a lineup by himself, and you saw a combination of guys buzz through another lineup."
Blue Jays: Sanchez (split fingernail) felt no pain and was "very encouraged" following a 33-pitch bullpen session. He is scheduled to pitch Tuesday at extended spring training and could rejoin the rotation after that. ... Happ (left elbow) is throwing from 90 feet on flat ground.
Rays: SS Matt Duffy (Achilles tendon surgery) continues running the bases and could be nearing a minor league rehab assignment.
Blue Jays slugger Jose Bautista went 0 for 13, including seven strikeouts, in the series. His batting average dropped to .174.
END OF THE ROAD
Ezequiel Carrera made a nice play in left field as a defensive replacement, but his hitting streak ended at a career-high 12 games. He entered in the eighth for Steve Pearce and justified Gibbons' move by making a running catch of Dickerson's drive with one out in the inning. Carrera, however, struck out in the ninth to end his streak at the plate.
Blue Jays: RHP Marcus Stroman (2-2) is scheduled to start Monday night against Cleveland RHP Trevor Bauer (2-3). Stroman was pulled after three innings, his shortest start in three years, during the Blue Jays' 8-6 loss to the New York Yankees on Wednesday night because of tightness in his right armpit.
Rays: LHP Blake Snell (0-2) will face Kansas City RHP Nate Karns (1-2) on Monday night. Snell has gone five innings or fewer in five straight starts, and nine of his last 10.