Soriano and Anthony cracked back-to-back solo shots in the first inning for an early Cubs lead and Chicago never looked back in racking up a fourth straight victory.
Travis Wood (6-6) yielded two runs on four hits over 6 2/3 innings to record the victory, walking two and striking out five.
The Angels' Joe Blanton (2-11) was tagged with loss, coughing up six runs on eight hits over five full frames.
Albert Pujols went 2-for-4 with a two-run homer for Los Angeles, which dropped the first of a two-game set.
2014: The Year in Music [PHOTOS]