"Can't put into words the appreciation I have celebrating on this field," Cobb said. "I knew how close it was to not coming back. Sitting on the couch watching these games, I knew we had a good chance. We have a great team. I was going to do everything I could to get back and be a part of it."
Delmon Young homered in the third inning off rookie Danny Salazar as the Rays, playing in their third city over four days, advanced to face the AL East champion Red Sox in the division series starting Friday.
"I felt like we've done it and been here before," said Desmond Jennings, who hit a two-run double. "The road we took to get here was pretty tough, going to New York, Toronto, playing a game in Texas."
Cobb's comeback in August from his frightening injury helped stabilize the Rays, who have spent the past two weeks winning crucial games to reach the postseason for the fourth time in six years.
Cobb pitched out of massive jams in the fourth and fifth, and allowed two runners to reach in the seventh before turning it over to Tampa Bay's dependable bullpen.
Joel Peralta struck out Nick Swisher on three pitches, ending Cleveland's last real chance.
Fernando Rodney worked a perfect ninth, striking out Lonnie Chisenhall to end it. Rodney dropped to one knee, pointed skyward and soon was mobbed by all the Rays, who may be a little homesick but are Boston-bound.
"Go out and play our game," Jennings said. "It's going to be tough anytime you play Boston."
Unfazed by a raucous, red-clad, towel-waving crowd of 43,579 that roared like a jet engine inside Progressive Field, the Rays handled the Indians and will now face their division nemesis, the Red Sox, who went 12-7 against Tampa Bay this season.
David Price set the tone for the Rays' postseason run by throwing a complete game to beat Texas in the wild-card tiebreaker Monday night, and Cobb picked up where his teammate left off. After he was pulled in the seventh, Cobb walked to the dugout where he was first greeted with a high-five from Price.
"The adrenaline was going pretty fast there in the early going," Cobb said. "Once Delmon hit that home run, I tried to fill up the strike zone. My stuff wasn't the best, but I made my defense work. They were awesome."