Captain Paul Wotton, celebrating his 25th birthday, proved Plymouth's late match winner for the second successive game when he powered home an 82nd minute pile-driver to defeat ten-man Luton.
Winless Luton, who were reduced to ten men in the eighth minute when Chris Coyne was sent off for a professional foul, looked set for a point after Steve Howard had levelled Brian McGlinchey 56th minute opener.
Plymouth Manager Paul Sturrock made one change to the side which beat Huddersfield 2-1 in midweek, bringing in midfielder Jason Bent for Lee Hodges.
David Bayliss was soon in the action though, coming on as an 11th minute substitute following the sending off of fellow centre back Coyne.
Coyne was dismissed for pulling back Michael Evans as the Argyle striker bore down on goal after latching on to McGlinchey's throughball. Striker Tony Thorpe was Luton's sacrificial substitute as manager Joe Kinnear reorganised.
Argyle however, struggled to make their numerical advantage tell and Luton, looking to hit their hosts on the break, nearly stole something when Robinson narrowly failed to get a touch to Matthew Spring's pass.
It took the home side 11 minutes of the second half to make the breakthrough and when they did, it was in spectacular fashion, McGlinchey powering in a left-foot shot from 25 yards after Davis had failed to clear a corner.
Luton levelled the scores in near identical style, when Howard ran at the Plymouth defence before unleashing a left-foot strike from the edge of the penalty area.
Just as it seemed Luton might earn their first point of the season, Wotton conjured up yet another thunderous effort after collecting a short throw from McGlinchey and powered the ball pastd goalkeeper Carl Emberson from 25 yards