That's a trend Chicago wants to continue, even with slugger Jose Abreu on the disabled list.
With Jose Quintana seeking some rare run support, the White Sox will try for their fourth win in five home meetings Monday in the opener of a three-game set with the last-place Indians.
Chicago (25-27) dropped 17 of the 19 meetings with Cleveland (24-27) in 2013, totaling only five home runs and 27 runs over the final 12 of a 14-game losing streak in that season series.
However, it's been a much different story for the White Sox in 2014. They've put up 35 runs with nine homers while winning four of the first seven - including three of four at U.S. Cellular Field from April 10-13.
"You've got to worry about yourself and executing what you can control," outfielder Adam Eaton told the team's official website. "I think we let the media and even the fans worry about who's coming into town and what they're throwing at us."
Abreu, tied for second in the majors with 15 home runs, has hit a team-high four against the Indians. The Cuban rookie, though, isn't expected to return until June because of tendinitis in his left ankle.
Alexei Ramirez could step up for the White Sox since he went 7 for 16 with two home runs and six RBIs in the four-game home set last month. Eaton also played well, going 6 for 14 with a homer and three RBIs in that series.
Chicago, though, hasn't given Quintana (2-4, 3.67 ERA) much support since providing him with 21 runs in his first two starts. He's received 15 in his last eight after allowing three runs over 7 1-3 innings in Wednesday's 3-1 loss at Kansas City.
The left-hander is 2-0 with a 3.09 ERA in six career starts against the Indians. He limited them to one runs over six innings April 13, but did not factor in the decision as the White Sox rallied in the ninth for a 4-3 home win.
Michael Brantley, 6 for 13 with a homer when facing Quintana, extended his hitting streak 11 games Sunday when the Indians split a four-game set in Baltimore with a 4-2 loss. He's also batting .405 over a nine-game hitting streak versus Chicago.
Michael Bourn had two of the team's five hits as Cleveland lost for only the second time in seven games. The leadoff man has a .400 average over his nine-game hitting streak.
Nick Swisher returned after missing two games with a sore knee, though Asdrubal Cabrera missed a third straight start with knee and toe injuries before pinch-hitting in the eighth inning.
"(My knee) looks much better right now," Cabrera said. "My toe is a little worse."
Josh Tomlin (3-1, 2.91) makes his first start since May 17 after earning a win in three innings of relief Wednesday. The right-hander allowed one run and two hits with six strikeouts in an 11-10 victory over visiting Detroit.
Tomlin, 0-1 with a 4.42 ERA in three career starts against the White Sox, faces a Chicago team that fell to 7-20 when held to four or fewer runs following Sunday's 7-1 home loss to the New York Yankees.