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.
Jackson will make one more start Thursday in the Cubs' final game at HoHoKam Stadium. The team moves to a new site in west Mesa in 2014. The right-hander said the Angels were aggressive.
"They came out swinging," said Jackson, who gave up five runs and eight hits in five innings. "I left a couple balls out over the middle of the plate and they did a good job hitting the ball. I challenged hitters, and they got their hits."
Spring Training is entering the dog days, and Jackson is ready for the regular season to begin.
"Health-wise, I feel pretty good," the right-hander said. "If the season started tomorrow, I'd be confident where I am and I feel I can go out and do what I need to do to help the team win."
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: Lefty Chris Rusin may have been assigned to the Cubs' Triple-A Iowa team on Friday, but he'll get at least one more start Sunday at 3:05 p.m. CT against the Indians in Goodyear. It will be Rusin's fourth spring start and sixth game. He's given up 15 hits and walked one over 18 innings. Also expected to play Sunday are Anthony Rizzo, Alfonso Soriano, Starlin Castro and Darwin Barney. The game will be broadcast on MLB.TV, Gameday Audio and WGN Radio.