The Florida native escaped a first-inning jam via a 6-4-3 double play before surrendering two runs in the second on an RBI single by Juan Francisco and a sacrifice fly by Eric Hinske.
Rhymes, who missed two games after getting hit by a pitch on his right arm and fainting on the field in Wednesday night's game, booted a ball to get the Braves started in the third. But he quickly recovered by starting a 4-6-3 double play and making a diving backhanded grab of Brian McCann's shot through the middle, then throwing out the Braves catcher to end the threat.
Cobb seemed to draw energy from the third inning and began to settle into a nice rhythm.
"[I] started out trying to nitpick too much and then started getting comfortable in the third or fourth inning," Cobb said. "Just started letting it ... loose -- nice and loose -- and started hitting my spots better."
Matt Joyce provided all the offense the Rays needed when he connected on a 2-0 pitch from Randall Delgado with one out and the bases loaded, depositing the ball over the wall in center field for a grand slam. An enthusiastic crowd of 27,433 responded accordingly, as Joyce rounded the bases with, "It's a Granny," flashing on the scoreboard.
"I was trying to hit something hard in the air. I tried to hit a sacrifice fly -- at the worst -- and I hit it pretty well and [it] worked out," Joyce said. "Usually when a pitcher falls behind 2-0, they're gonna throw a strike or try to throw a strike. That's exactly what I was looking for, and it worked out. It was a good pitch to hit, and I hit it well."
Many of the Rays' hitters have complained the past two seasons about how well-hit balls seemingly die in the Trop's center field -- where they would fly out in other ballparks. That wasn't the case on Saturday.
"I've hit some balls really well to center that just haven't gone," Joyce said. "I really didn't expect that one to go, either, just because as well as I've hit a ball to center, it doesn't go anywhere. I figured it would be a double, at the worse he catches it and runs into the wall or something. But that's all I've got."
Joyce's third career grand slam gave the Rays three on the season, along with a 4-2 lead. Sitting on the bench, Cobb instantly became a huge Joyce fan.
"[Joyce's blast turned] the momentum right around into our favor," Cobb said. "We're already down by two, trying my hardest not to get down by three. Start to nitpick a little bit and being up by two runs, I'm able to let them put the ball into play, not worry too much about getting further into a hole."
The Braves saw a different Cobb after Joyce's homer.
"He mixed his pitches well, and he was aggressive with no one on base," Jason Heyward said. "Then, he became even more so when they took the lead. He was throwing all his pitches for strikes and he just made it tough for us, especially seeing him the first time out."
Cobb held the Braves to six hits while striking out six in seven innings to earn his first win of the season, further validating his belief -- and the Rays' -- that he is a Major League pitcher.
"He definitely has that attitude [that he belongs in the Major Leagues], not in a cocky way [but] in a very confident way," Rays manager Joe Maddon said. "He believes he belongs in the big leagues. ... We've felt he [belonged in the Major Leagues] all along. We only have so many starting pitchers."
Cobb provides the kind of pitching depth any organization longs to have, and the system worked perfectly in the Rays' favor in this case.
"He got his innings in [at Triple-A Durham], guy gets hurt, he comes up, does what he's supposed to do, that's outstanding," Maddon said.
Sean Rodriguez added to the lead with a solo home run off Cristhian Martinez to start the sixth.
After Cobb left, Joel Peralta retired the Braves in order in the eighth and Fernando Rodney pitched the ninth, chalking up his 13th save of the season to preserve the win.