He curbed the Royals on six singles in seven scoreless innings and Ben Zobrist had three hits and drove in two runs to help the Rays beat Kansas City 5-0 on Sunday.
Cobb threw 65 strikes in 81 pitches, but developed a small blister in the seventh inning that led to Rays manager Joe Maddon going to his bullpen. "It's unfortunate because his pitch limit was in great shape," Maddon said. "He had plenty left in the tank."
Cobb (3-0) struck out two and walked none to pick up the victory and lowered his earned run average to 2.57. He has allowed one earned run in 13 innings in two starts since being recalled July 18.
Relievers Cesar Ramos, Joel Peralta and Jake McGee held the Royals to one hit the final two innings to finish off the Rays' eighth shutout of the season.
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"It was a big disappointment," Cobb said of the blister. "I wanted to throw at least eight innings, maybe nine. We're short in bullpen. I would have liked to have been able to help that out."
It is uncertain whether the blister will prevent Cobb from making his start Saturday at Seattle. What is certain is he won't be going back to the minors. This is Cobb's third stint this season with the Rays. He said he used to sit at his locker wondering whether he would be tapped on the shoulder and told to report to Maddon's office for another trip to Triple-A Durham.
"I'll keep a lookout after every outing, but seven shutout innings never hurts your cause," Cobb said.
Cobb, a 2006 fourth-round pick, is unbeaten in his first seven major league starts, the first Rays pitcher to accomplish that.
"This is why we went to a six-man [rotation]," Maddon said. "This is the exact reason. You can't do it unless you have a pitcher that is that effective and big league-ready and Alex is. There's no tapping on the shoulder."
When Cobb gave up two singles to leadoff the sixth and seventh innings, he quickly worked out of the jams.
"No panic," Maddon said. "He threw strikes, let the defense play. He made the hitters swing the bat, wasn't walking people and getting into bad counts. That's why he was able to get through that relatively easy."
The Rays scored two runs with two out in the sixth on one hit, a Sam Fuld single, three hit batters and a walk. After Fuld's hit, Felipe Paulino hit Sean Rodriguez and Desmond Jennings with pitches to load the bases. Blake Wood replaced Paulino and walked Johnny Damon, scoring Fuld. Wood hit Zobrist with a pitch to bring home Rodriguez.
Paulino (1-4), who lost for the fourth time in his past five starts, gave up four runs on seven hits, while walking two and striking out six.
The Rays scored a pair of runs in the third with Evan Longoria driving in Damon with a single. Matt Joyce's sacrifice fly scored Zobrist with the other run.
Cobb did not allow a runner past first base until the sixth when Matt Treanor and Chris Getz led off with singles. Eric Hosmer and Mitch Maier opened the seventh with singles, but Mike Aviles grounded into a double play.
"We just didn't come to play today," Royals leftfielder Alex Gordon said. "I don't say this a lot, but we deserved to lose. We didn't do much. We just didn't show up to play."
The loss snapped the Royals' four-game winning streak, matching their longest of the season. The Royals have not had a winning streak of five or more games since Sept. 7-11, 2009 when they won five straight.
Rays CF B.J. Upton was held of the lineup as stories continue to circulate he would be traded by July 31. "I don't know where I might be going but I don't want to go nowhere." Upton said. "This is just a day off. It's becoming comical for me. It's something new everyday. It's gotten to the point where I just don't care. If it happens, it happens." ... C John Jaso, who is on the Rays 15-day disabled list with a right oblique strain, could join the club Friday in Seattle to workout with the team, but is not ready to be activated. Maddon said Jaso probably would need to go on a minor league rehab assignment before returning. ... SS Alcides Escobar, the only Royal to play in all the first 100 games, and RF Jeff Francoeur were given the day off. Aviles and Maier replaced the two. ... The Royals hit four Rays batters to tie a franchise record. It was the sixth time in club history with the previous being June 12, 2010 at Cincinnati. The Royals hit 10 batters in the six-game homestand.