Willson Contreras added a two-run homer and Tommy La Stella hit a solo shot for the Cubs in the first as each team went deep three times at Surprise Stadium.
Rangers starter Nick Martinez, a candidate for the team's fifth rotation spot, allowed two earned runs in two innings. But eight of the 12 batters he faced reached base.
"I wasn't quite in sync," Martinez said. "I executed some good pitches at the right time, I was able to minimize, and on those pitches I was better in sync with my mechanics.