The left-hander put himself on the national radar by throwing seven scoreless innings to pick up the win and followed it up with three strong innings in relief in Game 4 to finish with a 0.90 ERA in 10 innings.
But unlike fellow left-hander David Price's memorable run to the World Series as a rookie in 2008, it was bittersweet for Moore as the Rays were eliminated by the Rangers in four games in the ALDS.
Fast-forward two years, and Moore has established himself as one of the best young lefties in the game He will get another chance to add to his sparkling postseason resume when he takes the mound in Game 1 of the ALDS against the Red Sox at Fenway Park on Friday (3 p.m. ET, TBS).
"I think I'm a little more aware of the lineup," Moore said of his mindset now compared to 2011. "I think that the whole Major League level, the experience -- that stuff kind of leveled off a little bit to where it's not as new.
"I think a lot of that helped me in 2011, just not having any expectations for myself that year and just being in a situation. It kind of helped me be in the moment."
"We feel very confident about our pitchers pitching against anybody, and we've done well," Rays manager Joe Maddon said. "Part of that is we talked about that prior to the fact that our guys are used to pitching or playing in that venue, whether it's Yankee Stadium packed, Fenway Park packed, we kind of dig it."
Game 1 comes on the heels of Moore pitching in a must-win game against the Blue Jays on Sunday in what could've been the final game of the regular season for the Rays.
Instead, Moore improved to 17-4 with a 3.29 ERA on the season by giving up three runs on six hits over 5 1/3 innings in a 7-6 win that forced a tie-breaking Game 163 against the Rangers on Monday. It was the first of three win-or-go-home games for the Rays, who advanced to the ALDS by defeating the Rangers on Monday and the Indians on Wednesday in the AL Wild Card Game.
"That was all the high blood pressure, you can kind of feel your heart right through your shirt," Moore said about picking up the win in Game 162. "It was worth it. It helps make the moment a little more special."
Moore pitched well against the Red Sox in two starts during the regular season, going 2-0 with a 1.80 ERA in 15 innings. He gave up three runs in six innings in a 5-3 win at Tropicana Field on May 14 before throwing his first career shutout on July 22 at Fenway Park.
But after that gem against Boston, Moore made just one more start against the Yankees on July 28 before being placed on the 15-day disabled list with what was described as left elbow soreness on July 31.
Moore didn't return until Sept. 3, but he picked up right where he left off. He posted a 2.79 ERA in six September starts to finish the year on a high note.
And now he has the chance to keep it going against the division-rival Red Sox at Fenway Park in yet another pressure-packed start in the ALDS.
"We feel like our pitching is good," Rays outfielder Desmond Jennings said. "They have good pitching, too, so you know it's always going to be a battle playing those guys, especially in Fenway."