The Rays (89-71) entered Monday's action three games behind the Oakland Athletics (91-68) with three to play in the AL wild-card race. Tampa Bay must sweep Baltimore and hope Oakland is swept by the Texas Rangers to have a shot at the postseason.
Alex Cobb pitched a gem to earn the win. Cobb gave up a run on two hits in seven innings and struck out seven. Ben Zobrist was 2 for 3 with a solo home run, and Chris Gimenez was 2 for 3 with a two-run double.
Wei-Yin Chen took the loss for Baltimore, allowing four runs -- one earned -- on six hits in 6⅔ innings. The Orioles (92-68) have already clinched a playoff spot and slipped to a game behind the New York Yankees in the AL East. New York hosts the Boston Red Sox for its final regular-season series.
First pitch for Game 2 at Tropicana Field is set for 7:10 p.m. ET on Tuesday. Baltimore's Miguel Gonzalez is scheduled to pitch against Tampa Bay's James Shields.