Rangers also ended a run of 22 matches without a clean sheet and increased the Pilgrims' relegation worries.
Argyle, one off the bottom of the Championship table, remain seven points from safety and look destined for League One.
Rangers dominated the game and were awarded a penalty ten minutes before half-time, when Matt Connolly crossed from the right and Tamas Priskin appeared to be pulled to the ground by defender Kari Arnason.
Taarabt, on loan from Tottenham, made no mistake from the spot, sending keeper David Stockdale the wrong way to register his sixth goal of the season.
It was a deserved breakthrough for Rangers, who had earlier gone close when Hogan Ephraim had a shot saved by Stockdale and when Jay Simpson blazed wide after latching on to Taarabt's pass.
After going ahead, Rangers almost doubled their lead when Stewart headed over from Alejandro Faurlin's right-wing free-kick.
But Stewart did find the net four minutes after the break, heading home Taarabt's free-kick to put Rangers two up.
Faurlin fired wide and Taarabt over, before Simpson missed the target after being presented with a golden chance by a mix-up between Stockdale and Arnason on the edge of the area.
Simpson was then unable to connect with a cross by Ephraim as Warnock's side continued to push forward.
Plymouth never looked like scoring. Carl Fletcher's header over from Karl Duguid's free-kick was their only meaningful effort on goal.