Scott Hairston hit a tiebreaking solo home run and Alberto Gonzalez smacked a two-run double in a four-run seventh inning as the Cubs rallied to tie the game.
Brent Lillibridge tripled to open the seventh and chase Angels starter Joe Blanton. Nick Maronde then walked pinch-hitter Dave Sappelt, and David DeJesus hit an RBI double. Gonzalez, battling for a spot on the bench, delivered a two-run double, but was thrown out at third trying to extend his hit. One out later, Hairston connected on his home run.
Blanton gave up two runs on seven hits over six-plus innings.
Efren Navarro singled to lead off the Angels' third and scored two outs later on J.B. Shuck's double down the right-field line past a diving Anthony Rizzo.
Pitcher Edwin Jackson collected the Cubs' first hit of the game off Blanton with a two-out single in the third, but was stranded.
The Angels' Chris Iannetta and Brendan Harris each singled with one out in the fourth, and both moved up on a wild pitch by Jackson before scoring on Cousins' ground-rule double. The ball apparently got stuck in the padding on the fence in right field.
Blanton dropped a single in center to open the fifth and scored two outs later on Kole Calhoun's double that Hairston had a tough time tracking down in left.
Jackson, who will start the Cubs' second regular-season game April 3 against the Pirates, helped himself in the fifth when he singled with two outs, driving in Darwin Barney, who had doubled. But the Angels added another run in the sixth on Navarro's RBI double off Hisanori Takahashi, one of four pitchers fighting for the last spot in the Cubs' bullpen.
Nate Schierholtz added an RBI double in the Cubs' sixth.
The Cubs and Angels will meet again during the regular season in a home-and-away Interleague series. The Cubs travel to Anaheim on June 4-5, and the Angels visit Wrigley Field on July 9-10.
Up next: Jason Vargas toes the rubber on Sunday when the Angels host the Giants at Tempe Diablo Stadium at 1:05 p.m. PT on MLB.TV. Vargas, who lines up as the No. 4 starter, gave up five runs on eight hits in 5 1/3 innings against the Brewers in Phoenix and will be making his second-to-last spring start. Fellow lefty Barry Zito will go for San Francisco.
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.