* Advance to best-of-five ALDS against top-seeded Red Sox
* Starter Cobb and three relievers combine on shutout (Adds quotes, details)
Oct 2 (Reuters) - The Tampa Bay Rays continued to thrive on the road with a clinical 4-0 victory over a profligate Cleveland Indians in their one-game, wild card playoff on Wednesday to advance to the American League Division Series.
The Rays, who played their last eight games away from home and faced three successive must-win games in Toronto, Texas and against the Indians at Progressive Field, will be on the road again on Friday, starting a best-of-five series against the top-seeded Boston Red Sox.
"Three games in three difficult venues... all in enemy territory," Tampa Bay manager Joe Maddon told reporters. "I'm proud of my guys."
Tampa Bay starting pitcher Alex Cobb, 11-3 during the season, masterfully mixed a big curveball with his fastball and was supported by a home run from designated hitter Delmon Young and a two-run double by center-fielder Desmond Jennings.
He combined with three relievers on the shut out.
Cobb pitched into the seventh, giving up eight hits and wriggling out of jams to spoil the party for the locals, who had finished the season with 10 straight wins to claim a wild card spot after losing 94 games last year.
The 25-year-old Cobb was not at his best but battled through, taking another inspiring step after missing two months due to a concussion after being hit in the head by a vicious line-drive back at him in June.
"You can't put it into words, the appreciation I have of celebrating out on the field," Cobb said.
"I know how close it was to not coming back. When I was sitting on the couch watching these games, I knew we had a chance, I knew we had a great team and I would do everything I could to get back and be a part of it and feel this celebration that we're doing right now."
Cleveland's hard-throwing rookie Danny Salazar retired the first six Rays batters, striking out three, before Young blasted a home run to left on the first pitch of the third inning for a 1-0 Tampa Bay lead.
The Rays added two more runs in the next inning off the 23-year-old Dominican.
Ground singles by James Loney and Evan Longoria set the stage for Jennings, who ripped a double down the third base line into the left-field corner for a 3-0 advantage.
"Once Delmon hit that home run and I had some runs to work with, I just tried to fill up the strike zone," Cobb added. "My stuff wasn't the best it's been. I made my defense work and they were awesome."
The Indians failed to come up with the key hit with men on base, squandering a bases-loaded, one out opportunity in the fourth when Asdrubal Cabrera grounded into a double-play, and a first-and-third opportunity with one out in the fifth.
In the seventh inning, Cleveland had men on first and second with one out and again came up empty.
"He was making pitches," Rays third baseman Evan Longoria said about Cobb. "He had to get through some tough situations in a tough environment, and for him to be able to make those pitches it had to give confidence to everyone."
Cleveland out-hit the Rays, who added an unearned run in the ninth, 9-8 but left nine men on base in the game.
"We knew what we were getting into today and they outplayed us," Indians manager Terry Francona admitted. "Congratulations to Joe (Maddon) and the Rays. They outplayed us.
"We were excited about coming into the game and we lost. Now we have to go home. It hurts."
The other American League Division Series will also get underway on Friday, with the Detroit Tigers visiting the Oakland Athletics. (Reporting by Larry Fine in New York; Editing by John O'Brien)