Edwin Encarnacion hit his 35th home run as the Blue Jays handed the Rays their sixth loss in seven games.
The Blue Jays have won three straight for the first time since July 26-28. Toronto went 9-19 in August.
The Rays lost for the 11th time in their past 12 one-run games, a stretch in which they lost four 1-0 decisions, and fell to 6-20 in one-run games since May 28. Tampa Bay also had its ML-worst 11th loss when allowing two or fewer runs.
That was the second runner of the game nailed at the plate. Matt Joyce was thrown out trying to score from second on Roberts' single to left in the second, with Rajai Davis picking up the assist.
Seeking to bolster their offense for the final month, the Rays acquired outfielder Ben Francisco from Houston for a player to be named. He'll join the team Saturday.
Starting for the
Morrow (8-5) allowed one run and eight hits in 6 2-3 innings. He walked one and struck out five and threw 102 pitches, 67 strikes.
Steve Delabar came on after Desmond Jennings hit a two-out double in the seventh and got B.J. Upton to ground out.
Delabar struck out the side in the eighth before Janssen finished for his 19th save in 22 chances.
The Rays opened the scoring in the third on a leadoff home run by Jennings, his 11th, but Toronto answered in the bottom half when Sierra drilled a leadoff shot off Jeremy Hellickson.
Encarnacion broke the deadlock when he hammered a ball into the second deck in center in the fourth. The homer was the fourth surrendered by Hellickson in his past two starts; he also gave up two in a loss to Oakland last week.
Hellickson (8-10) allowed two runs and four hits in six-plus innings. He walked one and struck out two.
NOTES: The Rays must add Francisco to the 40-man roster, meaning a roster move will be made before he joins the team. ... Tampa Bay will activate RHP Jeff Niemann off the 60-day DL Saturday to start against Toronto. Niemann has not pitched since a May 14 start against Toronto after fracturing his right leg when he was struck by Adam Lind's liner. ... The Rays also plan to recall INF Reid Brignac, C Chris Gimenez, LHP Cesar Ramos and OF Rich Thompson when rosters expand Saturday. ... Toronto 3B Brett Lawrie, out since Aug. 9 with a strained ribcage muscle, has resumed swinging after being shut down last week, manager John Farrell said. There is no timetable for his return.