The postgame scene, however, was dominated by the news of Liriano's acquisition. The lefty was traded to Chicago on Saturday night for Escobar and minor league left-hander Pedro Hernandez.
"He's such a good kid," Dunn said of Escobar, "We really enjoyed having him."
Escobar, who started at short in place of Alexei Ramirez, helped the White Sox pull away in a three-run fifth that extended their lead to 5-0.
Jordan Danks singled and came home on Escobar's double. Two batters later, Dunn hit a two-run shot that just cleared the wall in center.
Escobar also doubled in the seventh.
"Everybody loves (Escobar)," Chicago first baseman Paul Konerko said. "He's probably going to play every day and become a household name over there."
Konerko added a two-run homer for Chicago, which increased its AL Central lead to 2½ games over Detroit. The White Sox have won the first two in a three-game series between division leaders.
Humber (5-5) didn't allow a hit through three innings and won for the second time in three starts. He yielded one run, four hits and struck out four.
The Texas native was making his first start in his home state against the Rangers.
"I had a lot of friends and family here," Humber said. "It was definitely nice to pitch well here."
Matt Harrison (12-6), who lost his second straight start, gave up five runs and seven hits in seven innings. The left-hander walked three and struck out four.
Josh Hamilton sat out after Rangers manager Ron Washington elected to give his slumping slugger a mental break. Hamilton is batting .145 in July and heard rare boos from his home fans after striking out twice Friday night.
Mike Napoli had a solo homer and an RBI groundout for Texas, which dropped its fifth in a row to the White Sox. Humber and three relievers held the Rangers to five hits.
Texas went 0 for 13 with runners in scoring position and 1 for 21 in the series.
"If we start swinging the bat with some runners in scoring position, we can turn this thing around," Rangers manager Ron Washington said. "That's what's killing us right now."
The White Sox had two rookies and backup catcher Tyler Flowers in the lineup, but offensive leaders Dunn and Konerko came through with the big hits to sink the Rangers.
Harrison allowed only a walk through three innings before Chicago broke through. Dunn singled off Ian Kinsler's glove at second base with one out in the fourth. Konerko followed with a 416-foot drive to left, his 17th home run of the season.
Konerko is 10 for 19 with three home runs and seven RBIs over his last five games.
The White Sox broke the game open with their three runs in the fifth.
After losing five in a row, the White Sox have responded by scoring 40 runs during their current winning streak.
"You have to zone (Harrison) up and have a plan on what you're doing," Dunn said. "If you get away from the plan, he's going to get you."
Young tripled leading off the seventh and Napoli followed with a walk that ended Humber's night.
Jesse Crain inherited the first-and-third jam. He struck out Martin and Craig Gentry, then got some help from his defense. Dayan Viciedo made a diving catch of Kinsler's looping fly in shallow left to end the inning.
Chicago OF Alejandro De Aza (sprained left wrist) and SS Ramirez (bruised left hand) didn't play one day after being involved in a scary outfield collision. While neither injury is considered serious, White Sox manager Robin Ventura said De Aza likely wouldn't play Sunday, either. ... C A.J. Pierzynski missed his fourth straight game with a right oblique strain. ... Texas RHP Neftali Feliz will make his fourth rehab appearance Sunday for Triple-A Round Rock. He is expected to throw about 80 pitches. ... Chicago's Gavin Floyd (8-8) will face Texas' Scott Feldman (4-6) in the series finale Sunday.