The 26-year-old southpaw allowed just two hits -- a pair of solo home runs -- in six innings en route to his fourth quality start in five chances. Still, he took his third loss of the season.
"He's gone out and given us a chance to win, and certain games he's been borderline dominating," Rays manager Kevin Cash said.
In addition to being stingy with the runs, Smyly struck out eight batters, giving him 41 for the month of April and tying David Price's club record established in April 2014. He had a 2-2 count against Josh Donaldson in the sixth, but Donaldson homered to put the Blue Jays up 2-0.