With the victory, the Rays moved to 11 games over .500 to remain five games behind the American League East-leading Yankees.
Cobb delivered his fourth consecutive quality start, allowing one run on four hits with five strikeouts over seven innings. Rays starters are now 11-1 with a 1.72 ERA with 88 strikeouts in their last 15 games.
"I think Cobb was really the key," Rays manager Joe Maddon said. "Cobber was very good. And, as is typical for him, he's got better as the game was in progress. I thought his last two innings were his best again. He gets into a rhythm and all of a sudden starts making pitches. The curveball was outstanding again. And then the changeup, the depth at the end of the game before we took him out."
Cobb threw first-pitch strikes to the first 20 batters he faced.
"I was trying to attack the zone early and get ahead be able to expand the zone later in the counts," Cobb explained.
The only blemish on Cobb's line came in the fifth, when Trayvon Robinson tripled to open the inning and scored on Eric Thames' single. Rays catcher Jose Molina helped defuse a potential big inning by picking off Thames at first base for the first out.
Mariners manager Eric Wedge stated the obvious when he said his club "never really got anything going."
"Their kid threw a good ballgame, just had a sharp breaking ball, did a good job with his fastball," Wedge said. "Thought he commanded the baseball pretty good, as well."
Joel Peralta took over for Cobb in the eighth and struck out the three batters he faced. Peralta has allowed just one earned run in his last 15 1/3 innings. Fernando Rodney then pitched the ninth, getting the final three outs to preserve the win and earn his 37th save of the season. In doing so, the Rays closer converted his 22nd consecutive save, extending a club record. During those save opportunities, he has a 0.43 ERA while holding opponents to a .164 batting average with 22 strikeouts.
"The biggest thing as a pitcher, no matter what, is the outcome of the game," Cobb said. "You want to eat up innings. So being able to go out there and being able to set it up for Peralta and Rodney to close the door is a good feeling when you're walking off."
For the fifth consecutive game, the Rays' offense collected double-digit hits, which is the first time the Rays have collected 10 or more hits for five consecutive games since Aug. 28-Sept. 2, 2008. Five of Monday night's hits came in the third inning and led to the only four runs the Rays would score.
Desmond Jennings opened the scoring with an RBI single off Mariners starter Blake Beavan. B.J. Upton followed with a two-run homer to left field to make it 3-0.
"I think it was the right pitch, just bad location and with that guy, he just hits mistakes," Beavan said. "It was a mistake and he made me pay for it."
Upton was used as the Rays' designated hitter with Evan Longoria sitting out after six consecutive starts as the DH. Upton's home run gave him three in his last three games.
Ben Zobrist capped off the third with an RBI double to put the Rays up 4-0.
"They say [offense is] contagious, man," Upton said. "And that's the way it seems to be right now. We're swinging the bats well. And it's kind of something we've been waiting on all year. So hopefully we can do something the last two months."
Zobrist had three hits while playing shortstop for the fourth time in the Rays' last five games, and Matt Joyce extended his hitting streak to 12 games and Jennings extended his to six with two hits.
"It's a good run," Upton said. "Now we've got to keep doing what we're doing and try to come out and do the same tomorrow."