Home midfielder David Norris helped give Plymouth the perfect start by clipping the ball over the defence and beating keeper Simon Royce to the ball in the penalty area.
Royce – whose injury required treatment – was yellow carded for the challenge which resulted in Somerset referee Steve Tanner pointing straight to the spot.
Home skipper Paul Wotton kept his nerve after a three-minute wait to power home the spot-kick.
Wotton's third successful penalty conversion took his goal tally to four for the season.
Akos Buzsaky made a spectacular goal-line clearance to prevent QPR striker Kevin Gallen from levelling in the 10th minute.
Gallen's header, from Richard Langley's corner, looked goal bound until Buzsaky's intervention and subsequent chest-down to volley clearance.
Argyle added a deserved second in the 37th minute through Mathias Doumbe.
Buzsaky then had a 30-yard free-kick tipped over by Royce, who also used his legs to block Nick Chadwick's shot on the turn.
The Argyle striker did beat Royce with a glancing header from Buzsaky's quick 51st minute free-kick to make it 3-0.
QPR substitute Shabazz Baidoo scored with his first touch in the 61st minute, helping on an Ian Evatt header to beat home keeper Romain Larrieu. It was Baidoo's first goal for the Hoops.
Frenchman Larrieu was forced to tip over Gallen's header as the visitors sensed a comeback and nervousness in the home ranks.
But Tony Pulis' call for resilience was rewarded as Argyle held out for a well-merited victory.