One player who could emerge as a huge factor in the bullpen is Masterson, who missed most of September with a strained oblique, but threw three scoreless innings of relief upon returning.
Tampa, meanwhile, needed an extra game to get into this position, as it defeated Texas, 5-2, on Monday in a tiebreaker game to secure the second wild card spot.
"Get your 92nd win, you go to Cleveland against a really good ballclub," Rays manager Joe Maddon said after his team's win on Monday. "They're rested. I like the notion that we've pretty much been playing this (elimination-type) game for about a week now."
David Price went the distance for the fourth time this year and Evan Longoria belted a deciding two-run homer to pace the Rays, who are back in the postseason for the fourth time in the past six years.
"It's a whirlwind, like it always is," said Longoria, who was on base in four of his five at-bats. "We went through so much in the last three days, the ups and downs and the emotions, that it kind of feels like the whole season. We've had a lot of disappointment here, and to be able to celebrate here, it's pretty fitting."
Longoria could be getting hot at the right time for the Rays, as he is 11- for-19 (.579) with seven homers, 11 RBI and nine runs scored over his last five games.
Price (10-8), who came in sporting an ugly 10.26 ERA in four career starts in Arlington, made sure the Rays moved on by limiting the Rangers to two runs on seven hits. The ace struck out four, walked one and retired 11 of the last 12 batters he faced to finish off his gem.
"My last time against these guys, I beat them as well, so that kind of gets lost in it, just getting that first game out of the way," said Price. "Getting that first win against a team you've never beat, that's huge. Last time on this mound, I beat those guys. We did it again tonight. It's pretty special."
Getting the call for the Rays on Wednesday will be righty Alex Cobb, whose season was almost derailed back in June when he was hit in the face with a line drive.
The young hurler returned after missing two months and ended the year 11-3 with a 2.76 ERA. Cobb was unbeaten over the final month, going 3-0 with a 2.57 ERA and tossed seven scoreless innings his last time out against the New York Yankees.
"He pitched extremely well once again," Maddon said. "Curveball outstanding, changeup ... I think he was having a hard time command-wise with the changeup early. ... Then he started using his fastball more, which I thought was a great move. But overall, a fantastic performance."
Cobb is 2-1 with a 2.70 ERA in his career against Cleveland. This year, he faced the Indians once and beat them, 6-0, with seven shutout innings on April 6.
Pitching continues to be the Rays' calling card. They threw a team-record 17 shutouts this season, including four in their past 18 games. Their 32 shutouts over the last two years are tied with the Dodgers for most in the majors. They are the first AL team with 15 shutouts in consecutive seasons since the 1989-90 A's.
Tampa won four of its six matchups with the Indians this season.