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. With injuries to Scott Baker and Matt Garza, Rusin could be next in line if any of the other Chicago starters are sidelined.
"I don't ask questions," Rusin said. "I feel if I look too much into it, I won't be able to put the ball where I want it."
The left-hander did get off to a rough start but retired nine of the last 10 batters he faced.
"I had a rough first two innings and you never want that but it happens, it's baseball, and you just have to figure out your mistakes in the game," Rusin said. "I was able to figure out my release point and calm down and find my location and find my fastball and keep my offspeed in and out and keep them off balance. That's what Spring Training is for. You go out there and try to figure it out and what you need to do to get back on track."
Rusin has definitely been tested. He held the Indians and Dodgers scoreless over eight innings in his two previous outings.
"There's some tough lineups," Rusin said. "I know that. I just trust my catcher and hit the mitt."
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."
Cubs up next: After an off-day Wednesday, the Cubs will play their final split-squad games on Thursday. Half of the team will go to Tucson to face the Dodgers at Kino Stadium at 3:05 p.m. CT to raise money for the Christina-Taylor Green Memorial Foundation. Scott Feldman is scheduled to start and will be joined on the trip by Barney, Castro and Rizzo. Jeff Samardzija, the Cubs' Opening Day starter, will start Thursday night at 9:05 against the Mariners in Peoria. The Cubs-Mariners game will be broadcast on WGN Radio.