B.J. Upton had a career-high four hits, along with a run scored and an RBI for the Rays, who equaled their season high with 15 hits and improved to 3-18 in games decided by three or more runs.
Kazmir appreciated the support.
"The guys came through for us," said Kazmir, who improved to 3-2. "[It's] something about getaway day," the last game of a road trip, on which Tampa is 5-0 this season.
Kazmir said his command had gotten away in recent starts -- he needed 96 pitches to go five innings in his previous start, and he walked six the outing before that -- so he made a change. Kazmir, a left-hander, shifted where he stands on the pitching rubber -- going from the right side to the left -- to better follow through on his delivery.
"It took a little bit of time to get used to it," Kazmir said. "It was kind of a weird outing. I didn't throw any sliders. Maybe three or four. Mostly my fastball, two-seamer and change."
Kazmir wasn't perfect; the White Sox stranded two runners in the first inning and scored four runs after two outs in the third. He stayed the course.
"I kind of got out of rhythm in the third," Kazmir said. "As the game went on, I just kind of trusted the adjustment."
Pena's two-run home run tied the score at 4 in the sixth, and Crawford's sixth triple of the season landed the go-ahead run in the seventh for Tampa Bay.
Pena said he could feel a change in momentum after his homer, his 10th, which came against Javier Vazquez (2-3).
"When you come up with a game-tying or go-ahead hit, it definitely injects energy," Pena said. "Kazmir just took it and ran away with it. There's something to be said about momentum."
Pena's homer went to left, a sign of good hitting, he said, when one goes to the opposite field.
"It's not so much temptation, it's more of a natural 'reaction' to pull the ball," said Pena, who is batting .444 with five homers in his past 10 starts. "It's a lot of self-control and focus."
Crawford went 3-for-5 with two RBIs, extended his hitting streak to 10 games. Crawford is batting .388 in his past 21 games and has hit safely 19 times in that span.
Kazmir finished with seven strikeouts; his last, of Jermaine Dye, came after manager Joe Maddon visited him on the mound with two outs in the seventh.
"I wanted to show him that he was my guy in that situation," said Maddon, who had the bullpen going.
Chicago went 3-for-14 with runners in scoring position against Kazmir, who allowed four runs and eight hits with three walks. He threw 107 pitches.
"You just want to bear down and get more focused when it gets late in the game," Kazmir said. "You know the game's in our grasp."
The Rays, who earlier got a solo homer from Ty Wigginton, added six runs combined in the eighth and ninth against Chicago's bullpen. Tampa, which split the two-game, rain-shortened series, has 17 come-from-behind wins out of 20 total.
"I am extremely excited about what's going on here," Pena said. "I wish to be part of this. I think that the future's bright. We have a lot of talent and they're so incredibly young."