Leading the offensive explosion was third baseman Renato Nunez, who drove in five runs and scored two while falling a double short of the cycle.
After striking out in the fourth, Oakland's No. 16 prospect gave the AZL East champions a 3-0 lead with an RBI triple in the third that plated Herschel Powell.
The Dominican product drove in another run with a single in the sixth, then capped the scoring spree with a three-run homer in the bottom of the seventh to stretch the Athletics' lead to 14-3.
Nunez, who signed with Oakland in 2010 when he was just 16, ranked eighth among AZL hitters in batting average at .325 and third in RBIs with 42 in the regular season, but is not known for his power. Thursday's home run was just his fifth of the season.
Powell racked up three hits, three runs and two RBIs from the leadoff spot. Catcher Philip Pohl had a multi-RBI night as well, homering in the second to open the scoring and adding an RBI double in the A's seven-run sixth.
Designated hitter Trevor Gretzky, son of hockey great Wayne Gretzky, drove in two runs for the Cubs.
In other Arizona League action:
Rangers 7, Dodgers 3
The Rangers' Arizona League affiliate rode home runs by Nick Williams, Nomar Mazara and Alberto Triunfel to a 7-3 victory over the Dodgers that punched their ticket to the AZL championship.
Williams launched a three-run shot and 17-year-old Mazara -- whom Texas signed to a $4.95 million contract in June 2011 -- followed with a solo homer two batters later.
Luis Parra pitched seven four-hit innings, giving up just one run to earn the win for the Rangers. Box score