Argyle took the lead in the 13th minute when captain Paul Wotton unleashed a thunderbolt, but they had central defender Graham Coughlan red-carded within a few minutes.
Rangers centre-back George Santos followed Coughlan down the tunnel five minutes before the break and Argyle doubled their lead through man-of-the-match Mickey Evans within five minutes of the restart.
QPR quickly pulled one back from Paul Furlong's long-range free-kick, but Argyle held on for the points.
They were grateful to a linesman's flag for chalking off another Furlong effort, and then to French goalkeeper Romain Larrieu for twice denying Martin Rowlands in injury-time.
Wotton had already tried his luck from distance, dragging a low shot wide, before opening the scoring when he was teed up by Icelandic international midfielder Bjarni Gudjonsson, making his Pilgrims debut, for a spectacular strike.
Coughlan was the red-carded by referee Tony Leake, who later said that he had dismissed him for kicking Furlong.
Leake evened up the numbers five minutes before the break when he sent off Santos for a lunge on David Friio, and man-of-the-match Evans doubled Argyle's lead four minutes after the break, heading home Paul Connolly's cross.
Rangers reduced the deficit almost immediately after Gudjonsson was pulled up for a foul on the Hoops' half-time substitute Leon Best on the edge of the area, allowing Furlong to rifle home a low free-kick through the defensive wall.
Argyle should have extended their lead on the hour when Peter Gilbert slung over a fine cross from the left but although Marino Keith got a touch on the ball barely a yard from goal, he was unable to force it over the line.
Furlong went close in the dying minutes before Larrieu denied Rowlands low at his near post twice in the final minute of injury-time.