Dustin Brown gave the Rangers a 2-0 lead with a two-run homer off Chicago starter Ryan Dempster with one out in the Texas second.
Brown's homer came off a fastball that just missed its spot, Dempster said.
"That was really the only mistake today," he said.
Last year, Dempster got off to a rough start and was 1-3 with a 9.58 ERA in April. He's hoping to avoid that this season.
"I don't even think about games from then," Dempster said. "I'm focused on trying to get everything as sharp as I can and just worry about executing pitches. That's the difference between success and failure is executing pitches and looking at last year, that was probably the biggest problem was just lack of execution. I'm trying to do a better job of that now and hopefully by the time the season starts, it's right where I need it to be."
The Cubs tied the score in the fourth as Jeff Baker walked, advanced on a wild pitch, and one out later, scored on Blake DeWitt's triple. Reed Johnson's sacrifice fly tied the score at 2.
Dempster posted the longest outing by a Cubs starter this spring, striking out three and giving up two runs on four hits and two walks over six innings.
The Rangers received three scoreless innings from relievers Koji Uehara and Michael Kirkman, two potential key members of their bullpen. Kirkman had a 10.50 ERA going into the game but pitched two scoreless innings. He allowed one hit and struck out one.
Uehara has made five appearances and this is his first one without allowing a run. He suggested that his split-fingered fastball, an important pitch, is not as good as it needs to be, and it may be because of the dry Arizona air.
"I'm trying to get better," Uehara said. "I'm a command pitcher and I'm not comfortable with how I am throwing my split-fingered fastball. I'm not acclimated to the Arizona weather maybe."
Up next for Rangers: Michael Young takes an eight-game hitting streak into Thursday's split-squad doubleheader with the Cubs in Surprise and the Reds in Goodyear. Young is hitting .476 (10-for-21) with four doubles and two walks during the streak. Colby Lewis will start for the Rangers against the Cubs at 3:05 p.m. CT in Surprise in a game that can be seen on MLB.TV and heard on a free exclusive webcast. Scott Feldman will pitch against the Reds at 9:05 p.m. (CT) in Goodyear.
Up next for Cubs: After an off-day, Matt Garza will take the mound Thursday when the Cubs play the Rangers for the fourth time in six days in a game that can be seen on MLB.TV and heard on a free exclusive webcast. This will be Garza's fourth start. He's coming off a solid performance against the Giants in which he gave up three hits and walked one over four innings. Alfonso Soriano will be back in the lineup, batting third. He has four homers this spring, which ranks among the Major League leaders.