The Rays named Jake Odorizzi as their No. 5 starting pitcher after the game.
Delmon Young homered, singled and picked a catch off the top of the left field wall with the tying run on base in the eighth inning for the Orioles.
Young led off the second with the first spring home run against Cobb, who gave up six hits in his third start. Cobb struck out the side in the first inning and 67 of 88 pitches for strikes.
"It started to get a little bit tiring, but today as a whole is exactly what I needed," Cobb said. "All three pitches were working."
James Loney hit his second home run for the Rays in the first inning, driving in the only two runs off Baltimore starter Ubaldo Jiminez.
In his third spring start, Jiminez gave up five hits and a walk in six innings.
"I can't wait. I know I've only been here for a month, but spring training is long," said Jiminez, who signed with the Orioles as a free agent. "I can't wait for the season to start."
As the Rays' fifth starter, Odorizzi's spot in the rotation might be temporary. Jeremy Hellickson, who is recovering from January elbow surgery, is expected to return in late May or early June.