For the second straight day, the game ended with the potential tying run thrown out at home plate. This time, Colby Rasmus singled to center off Fernando Rodney, but catcher Jose Molina hauled in a high throw from B.J. Upton and blocked Omar Vizquel's path to the plate, tagging him out to end it.
Rays starter Jeff Niemann left in the fourth inning with tightness in his right arm, bringing an early end to his comeback from a broken right leg.
Niemann had not pitched since May 14 when he left a start at Toronto after being struck by Adam Lind's line drive.
J.P Howell got one out, Wade Davis (2-0) went 2 1-3, Jake McGee pitched the seventh, Joel Peralta got one out in the eight and Rodney got five outs for his 40th save in 42 chances.
Joyce drove in the deciding run by hitting his 15th homer, a second deck shot to right in the eighth off Brad Lincoln.
Edwin Encarnacion hit a two-run homer for Toronto, his 36th, but the Blue Jays failed to extend their modest three-game winning streak.
Beaten 2-0 in Thursday's series opener, Tampa Bay lost 2-1 Friday, a game that saw two Rays runners thrown out at home plate.
This time, Tampa Bay used a four-run, bat-around third to win for just the second time in eight games. The Rays also improved to 2-11 in their past 13 one-run games.
Roberts got the Rays on the board with a one-out drive to left-center, his third, off Henderson Alvarez.
Three batters later, Ben Zobrist's double scored Jose Lobaton. Evan Longoria walked to load the bases and Joyce followed with a two-run double to center.
Alvarez (7-12) lost for the fifth time in six starts, allowing four runs and five hits in five innings. He walked four and struck out two.
Niemann appeared to be walking around the mound in discomfort after Rajai Davis flied out to begin the fourth. Manager Joe Maddon and trainer Ron Porterfield came to the mound for a brief chat, and Niemann walked back to the dugout accompanied by Porterfield.
Niemann allowed one hit in 3 1-3 scoreless innings. He walked none and struck out four.
Howell came on and walked Rasmus, then gave up a towering homer to Encarnacion that hit off the facing of the fourth deck. Measured at 488 feet, it was the second longest home run in the majors this season. Miami's Giancarlo Stanton hit a 494 foot shot at Colorado on Aug. 17.
Encarnacion's blast snapped Howell's club record scoreless innings streak at 27 1-3.
Toronto cut it to 5-4 in the eighth when Adam Lind drove in two runs with a bases-loaded single off Peralta. Rodney came on and walked Yorvit Torrealba to load the bases again, then struck out Kelly Johnson and Moises Sierra.
NOTES: Rays minor league INF Will Rhymes was designated for assignment to make room for Niemann on the 40-man roster. ... After consecutive starts at 3B, Longoria was the DH Saturday. ... Tampa Bay LHP David Price (16-5) faces Toronto LHP Ricky Romero (8-12) in Sunday's series finale.