Jose Abreu went 2-for-3 with a double, triple and three RBI as the White Sox bested the Red Sox 4-1 on Tuesday.
Jose Quintana held the Red Sox to one run over eight innings in Tuesday's win.
David Robertson worked a perfect ninth inning against the Red Sox on Tuesday to earn his ninth save.
White Sox manager Robin Ventura said Tuesday that Alex Avila (hamstring) is close to rehab games.
Avisail Garcia (hamstring) is aiming to return to the White Sox starting lineup Wednesday.
Erik Johnson will join the White Sox starting rotation Thursday and face the Red Sox.
White Sox designated LHP John Danks for assignment.
Brett Lawrie hit a solo home run in Sunday's 7-1 win over the Orioles, the third consecutive game in which he has gone deep.
Chris Sale lacked his usual pinpoint control in Sunday's 7-1 win over the Orioles, walking four while allowing one run over 5 1/3 innings.
Avisail Garcia (hamstring) is not expected to be ready to play by Tuesday.
White Sox optioned RHP Tommy Kahnle to Triple-A Charlotte.
White Sox activated RHP David Robertson from the bereavement list.
Jimmy Rollins is not in the White Sox' lineup Sunday.
Jose Abreu went 2-for-5 with two RBI, including the game-winner in the ninth, as the White Sox outlasted the Orioles 8-7 on Saturday.
Brett Lawrie homered, stole a base and scored two runs in Saturday's win over the Orioles.