The Angels built a 7-2 lead but Chicago rallied for four runs in the ninth before reliever Fernando Rodney got the final outs and his sixth save.
Los Angeles starter Scott Kazmir (7-5) extended his personal winning streak to four games, lasting six innings and giving up two runs on five hits.
The Cubs got to the bullpen in the ninth when Francisco Rodriguez walked two and gave up a three-run home run to Tyler Colvin. Rodney entered the game and got two out but Derrick Lee connected for his second solo home run of the day, moving Chicago within 7-6 before a groundout by Geovany Soto ended the inter-league game.
The Angels got to Chicago starter Carlos Silva (8-2) for three runs and six hits in six innings. The first two runs came in the fourth with Hideki Matsui knocking in the first and Jeff Mathis getting Hunter home on a suicide squeeze play.
Chicago tied the score but Hunter's home run in the sixth made it 3-2 and Los Angeles had a three-run rally fueled by a pair of errors and Kendrick's two-run home run in the seventh.
Notable deaths of 2014 [PHOTOS]