Left-hander Brian Matusz fell behind, 1-0, just four pitches into his third start with the Orioles.
Johnny Damon launched a 1-2 slider onto the flagcourt in right field, his 27th career leadoff home run. The ball traveled an estimated 392 feet.
Damon has reached base in 37 consecutive games to tie the Rays record set by Ben Grieve in 2001.
Ben Zobrist and Justin Ruggiano followed with singles - Zobrist on a changeup, Ruggiano on an 88 mph fastball - and Evan Longoria's sacrifice fly increased the Rays' lead to 2-0.
B.J. Upton grounded a single into left field for Tampa Bay's fourth hit.
Matusz's fastball is topping out at 88 mph.
Instant update: Mark Reynolds' 13th error allowed another run to score. Rays 3, Orioles 0.
Matusz issued a two-out walk to Elliot Johnson, as the Rays sent nine batters to the plate. Matusz threw 33 pitches, 22 for strikes.
Tampa Bay stole four bases in the inning. Matusz has to do a better job holding runners. Catcher Craig Tatum didn't have a chance.