Currie, a recent £250,000 signing from Brighton, converted a controversial penalty for Ipswich midway through the second half, after referee Dermot Gallagher ruled that Darren Bent had been fouled by home keeper Romain Larrieu.
The midfielder then added a second five minutes from time after good work by substitute Jim Magilton and the goal proved vital for Ipswich as Mickey Evans immediately pegged back a consolation for the Pilgrims.
Argyle players were incensed with Gallagher's decision to award the penalty, claiming Bent had dived, but, in truth, the Pilgrims were lucky not to concede a spot-kick in the first half, when David Friio clearly pushed Ian Westlake.
Larrieu had kept Argyle in the game when he brilliantly saved at the feet of Bent midway through the first half.
New Argyle striker Scott Taylor, signed just after Christmas for £100,000 from Blackpool, went close with a header and a shot before Magilton's pass sent Bent away.
He outpaced Paul Wotton and went down under challenge from Larrieu, who was booked before being beaten by Currie's right-foot shot.
Magilton had come off the bench and proved a telling presence for Ipswich. It was his pass that unleashed Bent's fearsome pace.
With Wotton trailing in his wake, Larrieu had little option but to rush out of his goal and, when Bent pushed the ball wide of him and went over, Gallagher gave the spot-kick and booked the keeper.
Ipswich appeared to be coasting home when Magilton crossed for Currie to add a second, but Argyle's never-say-die attitude realised a goal when Paul Connolly centred for Evans.
His header was well saved by Kelvin Davis, who was helpless to prevent the follow-up shot.