DeLauter (wrist) will start in right field and bat second in Wednesday's game against the Orioles.
Vargas is absent from the lineup for Wednesday's tilt against the Pirates.
The White Sox placed Davis on the bereavement list Wednesday.
Burke (8-7) took the loss Tuesday against the Pirates after allowing seven runs on eight hits and two walks while striking out two over 1.1 innings.
Bibee didn't factor into the decision in Tuesday's 9-5 win over the Orioles, coughing up five runs on six hits and a walk over 4.1 innings. He struck out one.
Bazzana went 1-for-3 with a walk and a three-run home run in Tuesday's 9-5 win over the Orioles.
Martinez started in right field and went 2-for-5 with a triple and two runs scored in Tuesday's 9-5 win over Baltimore.
DeLauter (wrist) is absent from the lineup for Tuesday's tilt in Baltimore.
Lowe entered Monday's game as a pinch hitter and hit a three-run home run in a 6-4 loss to the Orioles.
Cantillo (9-9) took the loss against Baltimore on Monday, allowing four runs on three hits and two walks in 2.1 innings. He struck out three.
