Detroit has won 10 of 11 -- a run that's enabled the Tigers to stay atop the division despite a similar surge by second-place Cleveland.
"We can't control anything that other teams do, obviously," Fister said. "But we're coming in, playing hard and working together, and I think that's what's going to carry us anywhere we go this year."
The White Sox lost their eighth straight game.
Fister (10-5) allowed a run and seven hits, striking out two. Joaquin Benoit pitched a hitless ninth for his 11th save in 11 chances.
Iglesias, acquired from Boston this week in a three-team deal, started at third base in place of Miguel Cabrera, who experienced soreness after running and was scratched pregame.
Iglesias contributed right away with his new team.
"Baseball is the same," he said. "Great group -- and fun to win today."
Hector Santiago (3-7) allowed two runs and six hits in seven innings. He struck out seven and walked one.
"That was one of Hector's best games all year," White Sox manager Robin Ventura said. "He usually has an inning or two in the middle where he gets out of synch, walks a few guys and gives up some runs. That didn't happen today, and that's an important step forward for him."
Fister threw 88 pitches before being replaced by Benoit for the ninth. He won his fourth straight start -- and he's allowed four earned runs in 28 innings over that span.
Fister didn't strike out many batters, instead retiring them on groundball after groundball. That was one factor in keeping his pitch count so low.
"Things were feeling pretty good tonight," Fister said. "I'm trying to be as consistent as possible from Day 1, and things are falling our way right now."
The Indians lost Friday after eight straight wins, so Detroit now leads the division by three games.
The 23-year-old Iglesias was initially going to play second base Friday, but when Cabrera was pulled before the game, he moved over to third.
Iglesias could soon take over at shortstop for Jhonny Peralta, who faces a possible suspension amid the fallout from baseball's investigation into the Biogenesis of America anti-aging clinic. Peralta was in the lineup at shortstop Friday.
Prince Fielder led off the Detroit fourth with a double, and he went tumbling into third while advancing on Victor Martinez's flyout. One out later, Iglesias dropped a flare into shallow right field for a single to give the Tigers a 1-0 lead.
"I was just thinking -- put the ball in play," Iglesias said. "That's my goal -- see a lot of pitches, put a good swing and get a good pitch to hit."
Jackson hit his seventh homer of the year in the fifth, a high drive that carried over the fence in left-center field.
Chicago ended Fister's shutout bid in the sixth with an RBI single by Alex Rios, but Fielder cut off Jackson's throw from center and ran Rios down between first and second for the third out.
The White Sox (40-67) are at least 27 games under .500 for the first time since finishing the 1976 season 64-97. Chicago put the tying run on first to lead off the seventh and eighth innings, but each time, Fister was able to induce a double play grounder.
In the ninth, Rios drew a two-out walk and stole second, but Adam Dunn grounded out to end it.
The time of the game was 2 hours, 7 minutes. ... Both teams left men on first and third in the first. ... Detroit's Max Scherzer (15-1) takes the mound against Chicago's John Danks (2-8) on Saturday night.