Moore (15-3) made his first start in more than a month and notched a nifty one-hit start for the Rays, who had one win in their last nine starts coming into Tuesday's tilt in Southern California.
Moore, who had been sidelined with a stiff elbow, allowed one unearned run on four hits and four walks. The hard-throwing lefthander had won six consecutive starts before going on the disabled list.
The win moved Tampa Bay 2 1/2 games ahead of the Yankees in the AL wild-card race.
Jason Vargas (8-6) took the loss for Los Angeles after allowing five runs on 10 hits in four-plus inning. The Angels scored their only run in the second inning on a ground out by Colin Cowgill.
Swim Week Miami Beach 2014 [PHOTOS]