Prior to the Indians, the last team to do it was the 1971 Orioles.
Cleveland also went a major-league-best 21-6 in September. It was the first time Cleveland won 20 games in a month since doing so twice in 1995, a year in which the Indians reached the World Series.
"This is what you play for," Indians pitcher Justin Masterson said on Sunday. "You play to win a World Series, but you've got to get there first, get to the playoffs. So you play to get to the playoffs, and here we are with that opportunity. It's just been incredible. The ups and downs of this organization the last few years, we couldn't ask for anything better."
Hosting the game may also be a benefit for the Indians, who were 51-30 in front of their fans this season.
"It's been a long time since Cleveland's had something like this," Indians first baseman Nick Swisher said after Cleveland clinched the wild card spot on Sunday. "I hope the fans are as excited as we are."
The 92 wins for the Tribe were quite a contrast from a year ago when they lost 94 games. General manager Chris Antonetti made a bevy of offseason moves, but none may have been bigger than landing manager Terry Francona, whose leadership and calm presence has helped the Indians back to the postseason for the first time in six years.
"I have no doubt," Antonetti said, "that we would not be in the position we are without Tito's leadership."
As big of an impact as Francona has had on Cleveland, it was the team's starting pitching staff that carried them to the finish line. Cleveland's 3.16 ERA since the All-Star break was the second best in the American League and the fourth best in the majors.
During the 10-game winning streak, Indians pitchers held the opposition to two runs or less seven times.
One of those starters, right-handed rookie Danny Salazar, gets the call for the Indians on Wednesday.
"This is awesome," said Salazar, who has never faced the Rays. "The team has trust in me. I'm just going to do my best there."
Salazar has been brilliant since joining the rotation in July, boasting a 3.12 ERA, 1.13 WHIP and 65/15 K/BB ratio over 52 innings. He pitched to a 2.53 ERA in five September starts and recorded 33 strikeouts over 25 innings in that span.
"He's not a finished product," Francona said. "The finished product is going to be special, but he's comfortable on the mound. We wouldn't do it if we weren't comfortable."
If there's one drawback to Salazar it's the fact that the 23-year-old has pitched more than six innings in only one of his 10 starts.
So, Francona's bullpen will have to be ready and it's a unit without a leader at the moment, as the Indians will likely employ a closer-by-committee arrangement after Chris Perez was demoted from the closer's role following an awful final month that saw him pitch to a 9.64 ERA.
"I'm here to help the team," Perez said. "I went into (Francona's) office the other night and said, 'I'm not going to cost this team a playoff spot. You need to make a change right now. You've got four or five guys who are throwing the (heck) out of the ball. I don't have an ego. Make the change.' And he did."
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.