Warnock, who oversaw victory over West Brom in his first game in charge on Saturday, made it two wins in two to edge Rangers clear of the drop zone and deepen his old club's relegation worries.
The 61-year-old admits he is struggling to remember his new players' names, but the man he has christened 'Tarbs' put in a display he will not forget in a hurry.
Taarabt might not be wanted by parent club Tottenham but a host of scouts, including from Barcelona and Juventus, are keeping an eye on the 20-year-old.
He hit his sixth goal of the season from the penalty spot, and set up Damion Stewart for Rangers' second.
Warnock also succeeded where three previous managers have failed as Rangers kept a clean sheet for the first time in 25 games - although that said more about Plymouth's toothless attack.
Taarabt was a nuisance right from the first whistle, when he dispossessed Karl Duguid and teed up Hogan Ephraim who drilled in a 20-yard shot which was dealt with by Argyle keeper David Stockdale.
In the 18th minute Taarabt split the Argyle defence with a slide-rule pass but Jay Simpson, who has hit 13 goals this season, put his first-time effort wide.
Taarabt almost broke the deadlock with a piece of magic midway through the first half, when he was faced with three Argyle defenders on the edge of the box but wriggled free of all of them only to fire his shot into the side-netting.
But Taarabt made no mistake when given the chance from 12 yards in the 35th minute.
Kari Arnason clumsily pulled down Tamas Priskin in the area as they both challenged for Matt Connolly's cross and Taarabt sent Stockdale the wrong way from the spot.
Rangers could have gone two ahead moments later but Stewart headed Kaspars Gorkss' flick-on over the top.
Plymouth's best effort came in the first half when Alan Judge floated in a free-kick which former Hoops defender Chris Barker headed over.
Five minutes after the break Rangers went two up when Duguid felled Taarabt, who picked himself up to curl in the free-kick which Stewart headed home.
The hosts could have had more, with Alejandro Faurlin blasting over and also firing at Stockdale.
Simpson missed two gilt-edged chances, side-footing wide from in front of goal and then rolling a shot wide with Stockdale beaten.