Moore (10-3) logged a second straight victory after three consecutive losses, yielding just one run. The left-hander overcame six walks and allowed four hits in the triumph.
Desmond Jennings went 2-for-4 with an RBI single as Tampa Bay clinched its three-game home series.
Blue Jays starter Mark Buerhle (4-5) was touched for four runs on eight hits over five full frames.
Maicer Izturis got the only RBI for Toronto, which was held to just one run for the second straight game at Tropicana Field.
2014: The Year in Fashion [PHOTOS]
LeBron James reveals his new Nike shoes