Marlon Harewood's unforced penalty, Luke McCormick's soft own goal and Malky Mackay's tap-in meant it was game over before Teddy Sheringham's late second-half double rounded off the rout.
Following their FA Cup fourth round penalty shootout defeat at Sheffield United, West Ham brought back Sergei Rebrov and Hayden Mullins in place of Nigel Reo-Coker and the injured Luke Chadwick.
After drawing with rock-bottom Rotherham United, Argyle also made two changes as they recalled Steve Adams and Hasney Aljofree in place of Paul Wotton and Scott Taylor.
West Ham could not have asked for a better start when Graham Coughlan rose from a pack of bodies to inexplicably punch Rebrov's tenth-minute corner skywards, leaving Harewood - one of the villains of last week's spot-kick debacle - to calmly slot home the resultant penalty.
And when Rebrov sent over a low, in-swinging right-wing corner midway through the half, Plymouth keeper McCormick, under pressure from Mark Noble, somehow allowed the ball to deflect off his torso and inside his near post.
Rebrov limped away to be replaced by Reo-Coker but even so there was to be no respite for an Argyle defence so clearly inept at dealing with flag kicks.
When Noble's 39th-minute short corner was whipped into the box by Chris Powell, the curiously subdued Teddy Sheringham nodded on for the unmarked Mackay to hook over a woefully exposed McCormick.
Having received treatment, Aljofree was forced to wear a changed shirt with neither name nor number and at 3-0 down his team-mates must have wished for similar anonymity as they headed down the tunnel following an apathetic 45 minutes from Argyle.
A double substitution saw David Norris and Tony Capaldi emerge for the restart, while Steve Lomas and then Bobby Zamora stepped on for the Hammers.
Plymouth produced a little more fight and after 56 minutes, Stephen Bywater faced his first serious test of the afternoon when he somehow clawed out Nick Chadwick's point-blank effort.
With 15 minutes remaining the Hammers keeper made another brilliant double save to deny Mathias Doumbe and Dexter Blackstock before Sheringham woke from his slumber to turn the screw on the visitors.
First he met Carl Fletcher's centre with a powerful downward header and when the fleeing Reo-Coker was dragged down by the consequently dismissed Doumbe, the relieved Sheringham went some way towards atoning for last weekend's shootout miss when he sealed victory with a twice-taken penalty.