Roman Larrieu brilliantly tipped a shot from Kevin Horlock round the post, but was beaten from Currie's corner which James McEveley volleyed home.
Another Currie corner produced a second goal soon after as Jason De Vos headed the ball on and Jimmy Juan netted.
Akos Buzsaky curled a lovely free-kick into the top left corner but Larrieu brought down Nicky Forster to concede a penalty which Matt Richards converted.
Plymouth manager Tony Pulis:
"It is not going to be an easy job but I knew that when I took over. We need to bring in one or two players to help us out.
"Between the boxes we gave as good as we have taken but I was disappointed their first two came from corner kicks.
"We have discussed in the dressing room about players doing their jobs."
Ipswich: Price, Sito, De Vos, Naylor, McEveley, Currie, Horlock, Juan, Richards (Westlake 76), Parkin, Forster (Bowditch 60).
Subs Not Used: Supple, Magilton, Proudlock.
Booked: Parkin, Horlock.
Goals: McEveley 23, Juan 31, Richards 56 pen.
Plymouth: Larrieu, Connolly, Doumbe, Aljofree, Barness, Buzsaky, Wotton, Norris, Capaldi, Evans, Chadwick.
Subs Not Used: McCormick, Lasley, Taylor, Derbyshire, Djordjic.
Goals: Buzsaky 51.
Ref: M Atkinson (W Yorkshire).