The game was a makeup in a rained-out contest Thursday and allowed the White Sox to push their lead in the American League Central to three games over the Tigers.
Dunn led off with a single and advanced to third on Konerko's double before Alex Rios walked to load the bases.
After an out, Dayan Viciedo hit a grounder that shortstop Jhonny Peralta tossed to second for a force. But Rios went into second hard and Omar Infante's relay in an attempt at a double play was wide for an error, allowing Konerko to follow Dunn home.
Nate Jones, the second Chicago pitcher, improved to 8-0 in getting the win after a 2 2/3-inning, one-hit outing. The loss went to Doug Fisher (9-9), who was changed with all the runs -- four earned -- and eight hits in four innings.
Young had a two-run single to cap a three-run rally for Detroit in the third inning only to have DeWayne Wise, after a hit batter forced in a run, tie the score with a two-run single in the fourth.