Ball, who also netted in midweek against Notts County in the Capital One Cup, was at it again with a cracking 10th-minute strike after Argyle right-back Durrell Berry surrendered possession trying to clear down the touchline.
The ball was threaded back across the middle and the Fleetwood forward sent an unstoppable right-foot shot from 25 yards past goalkeeper Jake Cole.
Two minutes later Ball scored again from outside the penalty area with a wonderful, curling left-foot shot into the top corner of the net. Ball could have completed his hat-trick in the 18th minute after cutting in from the right but his angled shot, which beat Cole, flew just past the far post.
Plymouth's best chance fell to left-back Andre Blackman whose rising effort cleared the crossbar in the 87th minute.
Home Park boss John Sheridan responded to his side's poor display with a triple substitution in the 64th minute, introducing teenage striker Tyler Harvey, midfielder Luke Young and winger Andres Gurrieri.