Jackson allowed one hit and struck out three in 4 2-3 innings. The right-hander was hit hard in his previous outing after he had trouble finding Oakland's spring ballpark.
Jackson is competing for the last spot in the Cubs' rotation after going 6-15 with a 6.33 ERA last season.
Royals right-hander Edinson Volquez struck out eight in five-plus innings. He was charged with two runs and six hits.
Montero went deep in the first. Lake connected in the eighth against Wade Davis, who did not surrender a home run in 72 innings last season. Szczur hit his fourth spring homer in Chicago's four-run ninth off Royals closer Greg Holland.
