Harrison, who was battling allergies on a windy, dusty day, left at that point having thrown 81 pitches. His next start is on Sunday night against the Astros at Minute Maid Park in the season opener for both teams.
"I definitely didn't finish out the way I wanted to, but I feel like my stuff is there," Harrison said. "I'm ready to go. I just had a little trouble with my release point consistently today."
Sale got ready for his first start of the season by retiring 12 of 13 batters. The only hit was a home run by Geovany Soto in the third inning. Sale finished the Cactus League with a 3.86 ERA and with opponents hitting .210 off him. His first start will be on Monday against the Royals at U.S. Cellular Field.
"We are out of the getting-your-work-in stage and really starting to prepare for the season," Sale said. "We wanted to treat this as much like a regular-season game as I could."
The White Sox broke it open with five runs in the sixth against Rangers reliever Jason Frasor. Dayan Viciedo hit a three-run home run.
Sanchez and Short added back-to-back homers in the ninth off Texas' Ross Wolf. In the bottom of the ninth, Mitch Moreland hit a ground-rule double off Chicago's Hector Santiago to drive in a run and Craig Gentry plated another with a single.
Up next: Michael Kirkman pitches for the Rangers at 3:05 p.m. CT on Wednesday, live on MLB.TV and Gameday Audio, against the Angels in Tempe. Kirkman is getting the start because the Rangers want to stretch his innings out. He is still going to start the season in the bullpen. Nick Tepesch, who won a job as the club's No. 5 starter, will do his work in a Minor League game.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.