He did so by posting zeroes, nine innings' worth, in a 5-0 win over the Athletics at Tropicana Field. It's his first career complete game, as well as his first career shutout.
The Rays have now won 14 of their last 17 games to move within 2 1/2 games of the American League East-leading Yankees while maintaining their lead in the AL Wild Card race.
When last seen, Cobb was exiting stage right in Anaheim after surrendering eight runs in 2 2/3 innings. That was the night the Rays stormed back to score 10 unanswered runs en route to a 10-8 win -- effectively granting Cobb a no-decision.
Cobb made an astounding turnaround on Thursday, holding the Athletics to four hits to move to 8-8 on the season.
"That's a 'thanks' to the team and to the bullpen especially," said Cobb. "They had to carry me through six innings pretty much, so it felt pretty good to give them a break."
Cobb's shutout is the third of the season by a Rays starter, following those of David Price (April 24, against the Angels) and James Shields (July 31, Athletics).
The 24-year-old right-hander made a favorable impression on Athletics manager Bob Melvin.
"Just shut [us] down tonight," said Melvin. "We've been pretty good here offensively, but we just couldn't figure him out tonight. It was like every time we were looking for a fastball, he threw a breaking ball, and every time we were looking for a breaking ball, he threw a fastball, so he did a great job of mixing it up."
When asked about the dramatic difference between Saturday's and Thursday's performances, Cobb said he "stayed over the rubber a lot more" and "slowed things down" in his head.
"Just really thought about getting my arm over every pitch and driving to my direction," Cobb said. "Slowing things down is really what helped the most."
Rather than sulk or worry about that previous outing, Cobb felt a different emotion heading into this one.
"There was just an excitement all week," he said. "I'm really happy I felt that way toward it instead of being scared and wondering if I'm going to be hit around again. I was real happy the way I wanted to get the ball again and get back out there and compete and get a 'W.'"
Manager Joe Maddon wasn't surprised by Cobb's performance.
"Well, he's a tough guy, we know that about him," Maddon said. "It's just who he is, so it doesn't surprise me that he was able to bounce back like he did. He does not want to be embarrassed like he was his last outing. And he feels like he is a Major League pitcher. He was a big part of what we did last year, and he's doing it again this year. And he's getting hot at the right time."
A good sign for the Rays came in the fifth, when Evan Longoria -- making his second start of the season at third base -- backhanded Derek Norris' shot down the line and threw across his body to second baseman Ryan Roberts to complete an inning-ending force play.
In the seventh, Longoria stopped a wicked shot hit directly at him by Yoenis Cespedes, then threw a one-hopper to first that Jeff Keppinger picked for the first out of the inning.
"The ball that Cespedes hit was an amazing play," Maddon said. "The ball down the line with the accurate throw to second base, we've seen that a lot. He's able to throw accurately on the run to the second baseman covering. All that stuff is good.
"He's got to feel good about that mentally. He knows that he can do that stuff again. He also knows that his range and lateral movement aren't where they need to be yet, and he needs to know how to protect himself until he arrives at that point. But he answered a lot of questions, I think, too."
Longoria was making just his second start in the field since returning from the disabled list on Aug. 7. With him in the field, the Rays are able to use Luke Scott as designated hitter, giving the offense more firepower.
"When he's able to play there and we're able to do that more often, we can utilize the other guys as we'd like to more often," Maddon said.
That additional offense came to light in the fifth, when Scott hit a double that helped set the table for the big inning. Roberts had a sacrifice fly, Longoria and Sam Fuld had RBI singles, and Matt Joyce doubled home two more.
"We did a great job of putting together some hits, and usually when you string together some hits, some runs follow," Joyce said. "That's going to be our key, to string together those hits."
Joyce then tipped his cap to Cobb.
"For him to come back from his last start and pitch like he did tonight was really brilliant," Joyce said. "It's great to see a teammate out there come back from struggling a little bit and really carry the team. Obviously, doing what he did tonight, we're really happy and really proud of him."
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.