Jamie Mackie fired across Scott Carson to hand the troubled visitors an early lead before Gary Sawyer headed wide with the goal at his mercy as an upset threatened.
But the Pilgrims were made to pay for their wastefulness as Baggies centre-back Shelton Martis grabbed his second of the season from close range and Marek Cech found the top corner with a stunning strike to complete a first-half turnaround.
Both sides has chances after the break, with Argyle playing their part in a nervy finale at The Hawthorns, but Cech headed home to settle matters late on.
The result propelled unbeaten West Brom back to top of the table, however in stark contrast, winless Argyle sunk to their fourth successive defeat.
Simon Cox was handed his first league start for Albion as part of four changes made by Roberto Di Matteo - Chris Brunt, Graham Dorrans and Gianni Zuiverloon also coming in for Luke Moore, Jerome Thomas, Robert Koren and Shaun Cummings respectively.
Paul Sturrock also made four changes to his struggling Pilgrims side.
Defender Marcel Seip was left out altogether after he was transfer listed in midweek for a breach of discipline, with Darcy Blake, Alan Judge and Cillian Sheridan replaced by Reda Johnson, Karl Duguid, Steve MacLean and Luke Summerfield.
It was the visitors who started strongly with a clear point to prove following their recent troubles.
And they were rewarded with the opener after 12 minutes as Mackie eluded Martis down the left-hand side of the penalty area and beat Carson across the face of goal, despite the Baggies keeper getting a hand to it.
There was an edgy feeling around The Hawthorns as Albion went behind for the first time in the league this season.
Sawyer wasted a glorious chance to make it 2-0 midway through the first half, heading down but wide with the goal gaping.
Cox fired inches wide from the edge of the area at the other end as Albion threatened for the first time.
And the hosts gained their reward in the 34th minute as they upped the tempo, Martis getting the final touch on Jonas Olsson's near-post header.
Cech then found the net six minutes later, drilling a superb effort into the top corner from the edge of the area to cap off a great move from the Championship high-flyers.
Argyle emerged for the second half in all green shirts following a kit clash in the opening 45 minutes and a frantic spell of play kicked off proceedings.
Cech thought he had grabbed his second of the game minutes after the restart only to be judged offside with the home crowd celebrating.
And with play going from end to end at speed, Duguid saw his effort hit the crossbar from around 18 yards out.
Romain Larrieu did well to palm Dorrans' effort around a post before both sides rang the changes with the encounter degenerating into a tame affair.
The Pilgrims threatened to grab an equaliser as the game entered the closing stages but Cech headed a third for Albion to wrap up the points.