Tampa Bay has five games remaining on its schedule and is three games behind Oakland, which beat Seattle, for the second American League Wild Card.
On a night that saw the Rays get just three hits, they got off to a good start when Ben Zobrist homered off Gavin Floyd with two outs in the first. The 390-foot blast gave Zobrist 19 for the season while putting the Rays up, 1-0.
Unfortunately, the Rays looked snake-bit in the second when they experienced a combination of no clutch hitting and bad luck.
Luke Scott singled to lead off the second and Jeff Keppinger followed with a walk. After Carlos Pena went down swinging, Matt Joyce ripped a drive to right field that had extra bases written all over it. White Sox right-fielder Alex Rios had other ideas, though and made the grab at the wall.
"I actually thought that was a hit," Joyce said. "I was really surprised that he ran it down. I obviously knew I didn't get it all and it wasn't a home run. But when I hit it and saw where he was and where the ball was, I thought for sure it was a hit."
Maddon added: "That was a big play, but it wasn't a great play. It was a well-timed play. It was almost like he was well led. It was just fortunate for them that he could be there at the right time. ... That ball falls [and] that game can turn into a Rays victory."
Floyd, who got the win despite walking five in five innings, finished out the second by striking out Jose Lobaton.
"Today wasn't the sharpest day, but I tried to get out there and tried to put zeros up there any way I could," Floyd said. "That's my goal every time I go out there. It was a little more of a struggle today, but the bullpen did great. We had enough offense to win the game."
Chicago's offense finally kicked into gear in the third when Kevin Youkilis singled off Jeremy Hellickson to drive home Gordon Beckham. Rios then hit his 25th home run leading off the fourth to put Chicago up, 2-1. Rios' home run was the first allowed by a Rays starter in their last six games and just the second surrendered in their last 10 games.
Alexei Ramirez singled home Rios in the sixth to push the lead to 3-1.
"Here comes Ramirez, [Hellickson] makes a good pitch on him and he just fists it into left field," Maddon said. "That was a big play for them, obviously. That got them in the right direction."
Jesse Crain took over for Floyd in the sixth and silenced the Rays' bats for 2 2/3 innings before a parade of White Sox relievers successfully closed out the game.
"[Floyd] wasn't sharp," Maddon said. "It wasn't he was particularly sharp. We had opportunities and weren't able to get it done. That's just how the game works sometimes. You can play well and you can pitch well but just not get a hit at the right time. It's like they didn't do anything spectacular. But I thought Crain was the key to that game. Crain doing what he did permitted them to hold on to the lead and win that game."
Hellickson allowed two earned runs in 5 2/3 innings en route to his 11th loss. J.P. Howell, Wade Davis, Burke Badenhop and Cesar Ramos covered the final 2 1/3 innings, allowing no runs on one hit.
"We definitely pitched well enough to win tonight," Maddon said. "We just have to do a better job [driving in runs]. That's been the mantra the entire season. But it's not through a lack of effort. It's not through a lack of caring. We've just had those moments way too often this year."
Hellickson looked despondent about Friday night's results, but he, like others in the Rays' clubhouse, still believes the team can reach the postseason.
"We definitely needed a win, but we're not out of it yet," Hellickson said.
And looking ahead to the schedule, Hellickson is slotted to be the starter next Wednesday when the Rays play the Orioles in the final game of the season at Tropicana Field. A game that could still be significant depending on what unfolds over the course of the Rays' next four games.
"I hope so," Hellickson said.