The victory also prevented the Rangers from claiming the tiebreaker and home-field advantage in the AL Wild Card Game, should the two teams finish the regular season with the same record. They play on Thursday night to decide the season series.
Center fielder Desmond Jennings -- who misplayed a fly ball that allowed two runs to score 10 innings earlier -- was the hero as his game-winning single sealed the Rays' 11th walk-off of the season.
Jose Lobaton led off the 12th with a single up the middle before Yunel Escobar moved Sam Fuld, who pinch-ran for Lobaton, into scoring position with a sacrifice bunt. Then Jennings delivered.
"I definitely wanted to redeem myself," Jennings said.
It looked as though another Jennings misplay in center field would account for another Rays loss when Leonys Martin's laser line drive in the second froze Jennings. By the time Jennings raced back in an attempt to make a play, the ball was over his head for a two-run triple and a 2-0 Texas lead.
Instead, he was mobbed by his teammates three hours later, something Maddon feels can boost Jennings' confidence after he made two errors in September, more than he has committed in the prior two seasons combined.
"We all deal with maintaining our confidence daily with whatever we do, and when you're exposed like that in the middle of a baseball field, it bites you a little bit," Maddon said. "That play early in the game, I know he was seeking redemption at some point, and he got the opportunity."
Jennings, however, wasn't the only player who provided the Rays with a spark. Having given up its second lead of the game, Tampa Bay was down to its last strike in the 11th, but Matt Joyce escaped the at-bat by drawing a walk. Freddy Guzman -- who was just added to the roster Tuesday -- pinch-ran for Joyce and stole second base.
David DeJesus, another late-game replacement for left fielder Sean Rodriguez, collected the game-tying RBI with a single back up the middle off Rangers closer Joe Nathan, who blew his third save of the year.
"I didn't throw a bad pitch," Nathan said. "Could it have been better? Sure. But I'll take my chances with that pitch more times than not. He didn't hit it great, but he hit it enough to get it through the infield, get some outfield grass, put it in the right spot. … Tip my cap to those guys for battling with two outs and doing what they need to."
Somehow, the win also afforded a teachable moment for rookie Wil Myers. Before the Rays rallied in the 11th inning, Roberto Hernandez hit Elvis Andrus with a pitch in the Rangers' top half before Maddon gave the ball to reliever Alex Torres. Adrian Beltre delivered a two-out single off Torres, and Andrus surprisingly scored all the way from first when the throw from Myers, who was lackadaisical in retrieving the hit, only went to second baseman Ben Zobrist, whose relay to the plate was late.
"I should have been more aware of the situation and who was running," Myers said. "I should have charged the ball with more aggressiveness. It's one of those things you learn from and don't let happen again."
Lost in the shuffle was Rodriguez's game-tying two-out, two-run home run in the sixth off Texas starter Derek Holland.
Both starters limited the damage and gave up just two earned runs apiece in six innings, but Holland did it in a more efficient manner. Right-hander Chris Archer tossed 92 pitches, while Holland threw just 72.
With so many players contributing to the improbable victory, Maddon, who is always careful to not put more importance on one game over another, saw Wednesday's win as something more.
"I want to believe this game has to give us some kind of impetus moving forward," he said. "Two outs, nobody on against their closer and you get to two strikes on the hitter after the new guy steals second base? That doesn't happen every day. I want to believe all that stuff is going to give us some kind of push."