The loss was their 14th consecutive to the Indians and made their road record 26-55 this season, the most road losses in franchise history.
The Sox took a 1-0 lead in the second when Avisail Garcia hit a solo home run – his seventh of the season – to left center field.
The Indians answered with two runs in the bottom of the second on third baseman Marcus Semien‘s fielding error and a Michael Brantley RBI single off Sox starter Dylan Axelrod (4-11,5.68 ERA) to take a 2-1 lead.
Nick Swisher hit a two-run homer in the fifth to push the Indians’ ahead 4-1.
Axelrod went 5 2/3 innings, gave up eight hits and five runs – three earned, struck out one and walked two.
Salazar allowed two earned runs on six hits over 5 1/3 innings, struck out eight and walked one.
Paul Konerko was out of the Sox lineup with a bruised right kneecap he suffered on Tuesday night after fouling off his knee. Second baseman Gordon Beckham also was out dealing with a quad injury, and designated hitter Adam Dunn sat out for his fourth game in the last five.
The Sox must earn one victory in their final four games to avoid 100 loses.
Sox right-hander Andre Rienzo (2-2, 5.04 ERA) and Kansas City Royals right-hander Jeremy Guthrie (14-12, 4.09 ERA) are the starters for the Sox final three-game series opener of the 2013 campaign at 7:10 p.m. CT (CSN/WSCR 670).