Alexei Ramirez had a borderline chance of making the team's Opening Day roster.
In a span of six months capped by Monday's 8-2 makeup game victory over Detroit, that threesome has given the Sox a reasonable chance to advance to the American League playoffs for the second time in four years.
Floyd won his 17th game by pitching six innings of five-hit ball, throwing 118 pitches on three days' rest.
Ramirez made a last-ditch effort for the AL Rookie of the Year Award by smacking his fourth grand slam of the season, which broke a 2-2 tie in the sixth.
And young Hahn made Tuesday's 6:30 p.m. tiebreaker game against AL Central rival Minnesota more comforting to the Sox and their fans by correctly telling his father to call "heads" in a coin flip 2½ weeks ago, which gave the Sox home-field advantage over the Twins in a tiebreaker for the right to advance to the playoffs.
Tuesday's game was sold out less than an hour after Monday's victory and presents more support for the Sox, who were swept last week at Minnesota but went 7-2 against the Twins at U.S. Cellular Field.
"You get past feeling tired and the aches and pains," reliever Scott Linebrink said. "It's the adrenaline that keeps you going. And it's great to be in this situation after 162 games. It's going to take one extra game, and we wouldn't want it any other way."
Especially after the streaky Sox won consecutive games for the first time since sweeping a doubleheader from Detroit on Sept. 15 and stopped a five-game losing streak that nearly cost them a shot at advancing this far.
"You've got to dig down," first baseman Paul Konerko said. "You've always got more than you think, so you've just got to. If anyone is worried about [fatigue], then we're not focused. They're tired too, believe me. You just keep fighting."
The Sox overcame a masterful effort from former teammate Freddy Garcia, who limited them to two hits through five-plus innings before leaving with tightness in his right shoulder.
"The first time I stepped in the box I started laughing," A.J. Pierzynski said. "He cursed at me in Spanish, and I started laughing just because I know Freddy so well and I know he's back and throwing the ball great. I hope Freddy has a great career."
But Garcia's injury was a break, as Ramirez capped a five-run rally with a grand slam on the first pitch from Gary Glover.
"One thing about Alexei, he's not scared," manager Ozzie Guillen said of Ramirez, who has 21 home runs and a .290 batting average. "He doesn't know what kind of game this is."
Floyd, however, was nervous from the outset, Pierzynski said.
But he overcame his throwing error, which put the Tigers ahead 2-1 in the sixth.
"If you're not nervous in that situation, there's something wrong with you," Pierzynski said.