He made a career-high 11 starts and 25 appearances with the Rangers in 2008, but appeared in just five more games over the subsequent two seasons with the Rangers and Royals.
Mendoza spent the early portion of 2011 in the minors and was 12-5 in 33 appearances at Triple-A Omaha before returning to pitch seven innings of two- run ball in a 10-2 win over Detroit on Sept. 20.
He's 1-1 in three career meetings with the White Sox.
For Chicago, righty Gavin Floyd again looks for a first win of the season's final month.
The 28-year-old former first-round draft pick was 12-10 in 2011 after a 9-3 win at Seattle on Aug. 28. He's 0-2 in four September starts, however, including a 4-3 loss at Cleveland on Sept. 20 in which he allowed seven hits and four runs in 6 2/3 innings.
Floyd is 3-7 against the Royals in 13 career appearances.
On Saturday, Alex Rios had three hits, including a two-run homer, as the White Sox won, 6-3, in the second game of the three-game set.
John Danks (8-12) lasted 7 1/3 innings, allowing three runs on six hits and a walk while striking out eight. He remains undefeated in 12 starts against the Royals, posting a 5-0 record.
"This is probably the best stuff I've had all year," Danks said.
Brent Morel also homered for Chicago, which snapped a five-game losing streak at U.S. Cellular Field.
Ernest Teaford (2-1) allowed five runs on six hits and three walks through five innings for the loss.
"I don't think I did very well at all," Teaford said about his performance. "I wasn't consistently down, I wasn't getting my offspeed over early in counts and I was just behind a lot."
Melky Cabrera drove in two runs for the Royals, losers in three of their last five games.
Kansas City is 10-7 versus Chicago this season.