The shutout was Jackson's first since the former Tiger threw a no-hitter on June 25, 2010, as a member of the Diamondbacks.
This time, Jackson (6-7) scattered nine hits and two walks, while striking out two.
Carlos Quentin went 3-for-4 with a home run for the White Sox, who have won three of four. Juan Pierre tallied four hits, knocked in a run and stole two bases to move past Monte Ward and into sole possession of 28th place on the all-time steals list with 542 career swipes.
Quentin began the second with a bang, ripping a 3-1 fastball over the fence in left to give the White Sox a 1-0 lead.
Pierre ripped a one-out single to left an inning later and promptly swiped second to move past Ward. An Alexei Ramirez groundout moved Pierre to third, and he came home one batter later on Paul Konerko's base hit to left.
Miguel Cabrera doubled with one down in the sixth and Victor Martinez followed with a walk. Both runners advanced on Jhonny Peralta's groundout, but Jackson induced Carlos Guillen, who returned from the 60-day disabled list prior to the game, into an inning-ending groundout to keep the Tigers off the board.
In all, Detroit stranded nine and was 0-for-6 with runners in scoring position.
Scherzer was replaced by Jose Valverde to begin the ninth and the White Sox took advantage, adding three insurance runs.
Quentin led off with a single and was replaced by pinch-runner Brent Lillibrigde, who promptly stole second. Valverde then intentionally walked A.J. Pierzynski and both runners advanced on a passed ball.
Gordon Beckham plated Lillibrigde and placed runners on the corners with a single to right, then stole second. A Brent Morel groundout scored Pierzynski and Pierre followed with a single to push across Beckham, sealing the final margin.
Prior to the game, the Tigers activated Al Alburquerque from the 15-day disabled list and Guillen from the 60-day disabled list. Alburquerque recorded the final out in the top of the ninth. Guillen went 1-for-4...Jackson recorded the third shutout of his career...The White Sox are 26-20 against teams with a winning record.