With the win, the Rays improved to 32-26 on the season and 5-2 on the current road trip, with the rubber game slated for Thursday afternoon.
Cobb allowed five hits in 7 2/3 scoreless innings en route to a no-decision; Fister went 8 1/3 innings, allowing all three runs to take his third loss of the season.
Fuld's bunt single leading off the ninth proved to be the beginning of Fister's undoing.
"I'm always kind of looking to see if there's an opportunity to bunt for a hit," Fuld said. "I noticed [Prince] Fielder was back a little bit [at first] -- not way back, but back enough that if I got it past Fister, I had a good chance."
Once Fuld got close to the bag, he made a head-first slide and just evaded Fielder's tag.
"That's just all instinct. You're trying to stay inside the baseline but avoid the tag at the same time," Fuld said.
Ben Zobrist followed with a single to right, moving Fuld to third. Matt Joyce's sacrifice fly then put the Rays on the board with the game's first run. Evan Longoria singled home another run and scored on Desmond Jennings' triple off Drew Smyly with two outs to put the Rays up, 3-0.
Fuld wasn't supposed to start on Wednesday night, but when Kelly Johnson experienced a spasm in his back, manager Joe Maddon opted to start Fuld and leave Johnson on the bench for possible use later in the game.
"Kelly did me a favor and gave me a head's up that I might need to go in there and start," Fuld said. "That was about 3:30 or 4. And I guess I got the official word about 5, when we were out there at BP. I was prepared. It was a good teammate move. I've been his caddy the whole season, so it's nice to have him return the favor to me."
The ninth inning felt like an anomaly based on the way both starters pitched. There were plenty of teases along the way, but neither team could mount anything offensively. In the end, the Tigers were shut out for the sixth time this season.
"It's an extremely tough team to do that against, so it's nice to be able to do that," Cobb said. "It was a hard-fought game the whole way. Doug Fister threw a great game against us. It was a battle, and those games are a lot of fun to be a part of and come out on top."
The Rays appeared to have something going against Fister in the third after Jose Lobaton doubled with one out and Yunel Escobar followed with a single. Fuld then grounded sharply to Fielder, who threw home to catch Lobaton in a rundown.
Catcher Alex Avila ran Lobaton back toward third before finally tagging him out. Alertly, Avila then reached down to tag out Escobar sliding into third base for a 3-2-2 inning-ending double play.
Twice when the Tigers threatened against Cobb, the Rays elected to pitch to Fielder rather than Miguel Cabrera in a "pick your poison" decision Maddon made because he, like a lot of managers, deems that Cabrera "is from another planet." Fortunately for the Rays, both times Maddon elected to walk Cabrera and pitch to Fielder, it paid off for the Rays.
In the sixth, the Tigers had a runner at second when Cobb issued the intentional pass to Cabrera before striking out Fielder swinging. And in the eighth, the Tigers had a runner at second when Cobb intentionally walked Cabrera. Joel Peralta then came in and finished the job by striking out Fielder to end the inning.
Fernando Rodney pitched a scoreless ninth to complete the shutout while earning his 12th save of the season.
Even though Peralta and Rodney got the last four outs of the game, Cobb was the story, starting after nine days of rest because of a small cut on his right middle finger. Clearly, he had no rust.
"I knew if I could gather myself and stay under control, it would be a good night because of how fresh my arm is," he said. "And that layoff definitely helped."
Cobb effectively got ahead in counts, which allowed him to set up hitters the way he wanted to, using his quality stuff to finish the job.
"It was pretty weird out there today," Tigers outfielder Torii Hunter said. "I usually don't tip my cap, but I have to tip my cap to him to shut a team down like this. ... He did what he had to do.
"It felt like Bugs Bunny was pitching today. When you swing the ball just drops out of the zone. It's like it didn't want to get hit."