But they came away winners thanks to David Price's complete-game effort and Evan Longoria's three hits, which led the way in a 5-2 win in the American League tiebreaker game on Monday night.
"It's a whirlwind, like it always is," Longoria said. "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 -- it's weird when it hinges on one game. Being able to come in here and go through this ballclub. ... We've had a lot of disappointment here, and to be able to celebrate here, it's pretty fitting."
The Rays finished their 163-game regular season with 92 wins, which proved to be enough to send them to the playoffs for the fourth time in six years.
"I think it really speaks well of us to beat them," manager Joe Maddon said. "I know they've gotten us in the past. It's our turn this year. And we just continue to move forward. Next year they'll be right back after it."
Tampa Bay will now play Cleveland in the one-game AL Wild Card Game on Wednesday night at 8:07 p.m. ET at Progressive Field in Cleveland in a game you can watch on TBS.
Price brought little success against the Rangers into this start, having gone 1-4 with a 5.98 ERA in eight career regular-season starts against them and 0-3 with a 4.66 ERA in three postseason starts, so he had something to prove against the team that had eliminated the Rays from their past two postseason appearances.
And the 2012 AL Cy Young Award winner did just that, allowing just two runs on seven hits.
"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," Price said. "Getting that first win against a team you've never beat, that's huge. Last time on this mound, I beat those guys ... and we did it again tonight. It's pretty special."
Maddon said Monday's win was "all about David."
"That was his best game against this club, best game in this ballpark," Maddon said. "During the course of the game, I kept talking to [catcher Jose Molina], and he said he was getting better and better, and I could see that from the side. There was no way I wanted to take him out. He was outstanding. I thought his stuff kept getting better."
Tampa Bay scored in the first inning for the fourth consecutive day when Delmon Young hit a sacrifice fly off Martin Perez.
Longoria pushed the lead to three runs with two outs in the third when he drove a first-pitch fastball from Perez 382 feet over the wall in right-center for a two-run homer, his 32nd of the season.
"I thought [Perez] did a good job," Texas manager Ron Washington said. "Yeah, they jumped on him in that first inning, but he minimized the damage."
Ian Kinsler singled off Price in the bottom of the third to drive home Chris Gentry and cut the lead to two runs.
Longoria added a one-out double in the sixth off Alexi Ogando and moved to third on Young's groundout. Pinch-hitter David DeJesus then doubled to right to drive home Longoria with the Rays' fourth run.
In the Rangers' half of the sixth, Elvis Andrus singled with one out and then stole second base. Alex Rios followed with a double off the left-field wall to drive home Andrus and cut the Rays' lead to two runs.
Young dropped a two-out blooper to center field that should have scored at least one run in the seventh, but left-field umpire Bruce Dreckman ruled that center fielder Leonys Martin made the catch, even though replays showed the ball bounced into his glove.
Sam Fuld made up for the lost opportunity on a head's-up play on the bases in the ninth with the Rays clinging to a two-run lead. Fuld singled off Tanner Scheppers to open the inning and moved to second on Wil Myers' groundout. With Ben Zobrist at the plate, Fuld took off for third. Once Scheppers realized Fuld was running, he appeared to rush, resulting in a wild throw to third that allowed Fuld to score.
"I knew [Rangers third baseman Adrian] Beltre was nursing a bad hammy, so I thought he might be slow to cover at third," Fuld said. "It was loud all night, and with the noise, it might take Scheppers longer to hear that I was going. And I had heard and I'd seen that he had trouble throwing to bases. I had that all working in favor for me. So I figured, why not take a chance?"
Fuld's daring gave the Rays a three-run cushion heading into the bottom of the ninth.
"That extra run really took any extra momentum out of their sail," Maddon said. "Sam's play was big."
Maddon couldn't hide how pleased and proud he is about his club's accomplishment in reaching the postseason.
"I'm really proud of our guys," he said. "I thought winning the game like we did Sunday would let us come out relaxed tonight, and that's what happened."