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.
Things got dicey in the ninth inning, as Kyle Farnsworth gave up two quick runs. Fernando Rodney came in and allowed two runners to reach base before retiring the side for his 47th save.
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.