After winning at Texas, 5-2, Monday night, in a tie-breaker for a wild card spot, the Rays headed to Cleveland to face the Indians, winners of 10 straight down the stretch and owners of the top wild card spot, thus the home field edge.
In the fourth, Desmond Jennings made it a 3-0 game driving in a pair of runs with a two-out double to left, scoring James Loney and Evan Longoria.
Cobb continued to work out of trouble, thwarting the Indians' attempts to get back into the game, leaving Cleveland with the bases loaded in the fourth inning and stranding runners on second and third in the fifth, after the Indians had players on first and third with no outs.
Cobb worked into the seventh, leaving runners on first and second with two down for reliever Joel Peralta, who got Nick Swisher swinging on strike three to end the inning. Cobb won his first post-season start, scattering eight hits over 6 2/3 innings, walking one and fanning five.
Jennings finished 2-for-3 with two RBI. The Rays tacked on a run in the top of the ninth when Yunel Escobar singled home Ben Zobrist.
Closer, Fernando Rodney, struck out two and didn't allow a baserunner in the ninth, a non-save situation, for the 4-0 victory.
With the win, the Rays earned the right to continue traveling on to Boston, where they will open the best-of-five divisional series with the Red Sox on Friday.
There were no games in the National League on Wednesday.
Best-of-five divisional series begin Thursday. Pittsburgh is at St. Louis beginning at 5:07 pm EDT, with A. J. Burnett facing Cardinals' ace, Adam Wainwright.
The LA Dodgers play at Atlanta, first pitch slated for 8:37 pm EDT. LA's Clayton Kershaw opposes the Braves' Kris Medlen. Both games will be broadcast by TBS.
Today's Trivia: What National League team fielded five rookies of the year in a row in the 1990s? (answer tomorrow)
Yesterday's Answer: Ryan Howard was NL rookie of the year in 2005 and won the MVP award in 2006. Boston's Dustin Pedroia was the 2007 AL rookie of the year and league MVP in 2008.