Anderson had a game-ending hit Wednesday against Minnesota. This time, he easily scored on Sanchez's single to right field off Joe Jimenez (0-2).
Juan Minaya (2-1) pitched a scoreless ninth to get the win.
Jose Abreu homered and went 2 for 2 with two intentional walks for Chicago. Jose Iglesias had a two-run single for the Tigers.
Detroit starter Justin Verlander allowed two runs and six hits in seven innings. Miguel Gonzalez gave up two runs and seven hits in eight innings.
Abreu's 26th home run in the first gave Chicago a 1-0 lead.
The Tigers took the lead in the fifth when Victor Martinez singled, Andrew Romine doubled and Iglesias had a bloop single.
Verlander struck out the side in the bottom of the fifth after getting the lead, but the White Sox rallied in the sixth to tie the score at 2. Abreu singled, moved up on a wild pitch and scored on a single by Avisail Garcia.
MONCADA ON DL
The White Sox put rookie 2B Yoan Moncada on the 10-day disabled list before with a bone contusion of his right shin. The 22-year-old is hitting .188 with three home runs and 11 RBIs in 30 games since being promoted to the major leagues last month.
Moncada missed two games last weekend with what was described as shin splints. He aggravated the injury Thursday night during a misstep on third base and left the game in the sixth inning.
"No one likes to be on the DL," he said through a translator. "You know what? I can't do anything about it. This is the best (move) for me. I have to rest."
Tigers: 3B Nick Castellanos was scratched about 40 minutes before the start with a sore left wrist.
White Sox: INF/OF Nicky Delmonico was scratched a couple of hours before the start with a sprained right wrist. He was injured during his third at-bat on Thursday night.
Chicago lefty Carlos Rodon (2-4, 3.88 ERA) faces righty Buck Farmer (2-1, 6.62) in the middle game of the series Saturday night. Rodon won his last start against Minnesota on Monday, allowing two runs on four hits in 6 1/3 innings. Farmer has given up five homers in 17 2/3 innings in four starts.