Olt and Baez hit back-to-back home runs in a five-run third, and all the runs came with two outs against Alexi Ogando. Ryan Kalish reached on an error by third baseman Kevin Kouzmanoff and Olt followed with an opposite field homer, his fourth. Baez then connected on his fourth, also an opposite field shot to right. Rafael Lopez singled and scored on Darnell McDonald's double, and Brett Jackson completed the cycle with a RBI triple.
"Mike put up a great at-bat and launched it, and Javy coming up behind him, very aggressive," Chicago starter Jason Hammel said. "It's a show of good things -- signs of good things to come. I'm very impressed with those guys. They're still very young hitters and they're going to learn even more and get even better. It's very good to see."
Ogando threw 35 pitches that inning, and went out to the mound to start the fourth but was pulled. The Rangers put together six scoreless innings from their relievers. That included one each from Joakim Soria, Jason Frasor and Neal Cotts. Soria and Frasor have not allowed a run in six outings this spring.
"They are doing a good job," Texas manager Ron Washington said. "They are doing exactly what they did last year, coming in, getting outs and pounding the strike zone."
Olt, who was the Rangers' first-round pick in 2010 and who was traded to the Cubs last July in the Matt Garza deal, added a sacrifice fly in the Chicago fourth.
Hammel gave up one hit in the first three innings, but with one out in the fourth, Kouzmanoff doubled and scored on Adduci's triple. Arenciba followed with a RBI single.
The Rangers added two more runs in the fifth on a sacrifice fly by Alex Rios and RBI double by Kouzmanoff.
Hammel, projected for the fourth spot in the Cubs rotation, served up four runs on seven hits and two walks over five innings. The right-hander said he felt strong at the end of his outing.
"The only thing that bugs me right now is the walks," Hammel said. "I've been walking too many guys. I've got to get the fastball command glove-side a lot better."
Adduci tied the game at 6 with a two-run homer in the eighth off Armando Rivero, who was assigned to the Cubs' Minor League camp earlier in the day.
The Cubs have less than two weeks remaining in the spring schedule before the season opener March 31.
"I know everybody is itching to get out of here and start playing some games that count," Hammel said. "It's that time of year to make sure you get your work in, don't do anything too crazy, stay healthy and get to Opening Day. That's what we're working on now. For myself, it's fine tuning things now and head to Chicago."
Up next: Robbie Ross is on the mound and Adrian Beltre is expected to return to the lineup on Thursday when the Rangers play the Reds at Goodyear. Beltre has been sidelined since last Thursday with tightness in his left hamstring but said Tuesday that he is ready to play. Beltre said he will be in the lineup on Thursday.