David DeJesus singled and reached third on an error by shortstop Luis Sardinas, who couldn't get a glove on Starlin Castro's grounder. Anthony Rizzo hit a sacrifice fly, and Soriano followed with his third spring home run to go ahead, 3-2.
The Rangers took a 4-3 lead in the second on an RBI single by Ian Kinsler and a sacrifice fly by David Murphy, but Darwin Barney tied the game with a one-out home run in the second off starter Alexi Ogando.
Castillo walked to open the Chicago sixth, and two batters later, scored on the passed ball charged to catcher Konrad Schmidt.
Rusin, expected to open the season at Triple-A Iowa, gave up four runs on seven hits over five innings, striking out five.
Ogando, who will be either third or fourth in the Rangers' rotation when the season starts, gave up three earned runs on five hits over five innings.
"Overall, I feel ready," Ogando said. "I have been focused on attacking hitters and I feel like I'm improving every day."
Rangers up next: Derek Lowe pitches against the Angels at 8:05 p.m. CT Thursday in Surprise. Lowe has pitched five scoreless innings in two starts since signing a Minor League contract with the Rangers. Left-handed relief candidates Joe Ortiz and Nate Robertson are also scheduled to pitch.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.