He went 0-for-3 with a walk as the White Sox lost 1-0.
Jones, who last led off with the Atlanta Braves on April 10, 1998, entered Sunday batting .215 with 10 home runs and 22 RBIs. He batted .259 with six home runs in April but cooled in May, batting .208 with three home runs.
Jones has batted in the Nos. 3-6 spots to this point this season.
The White Sox missed out on their fifth straight victory and their first three-game sweep of the Cubs at Wrigley on Sunday night.
Bruce Levine covers baseball for ESPNChicago.com.