The midfielder netted in the 28th and 42nd minutes to condemn Argyle to a first home defeat for six weeks.
Kevin Lisbie added a third three minutes after half-time before Argyle centre-back Craig Cathcart nipped in with a late goal to reduce the deficit.
The only sour note for the Tractor Boys was the last-minute sending-off of former Argyle midfielder David Norris.
Norris, who moved to Ipswich from Plymouth for £2.25million in January, was shown a second yellow card for kicking the ball away in injury-time, having previously been booked for a foul.
In all, referee Pat Miller, who had a poor game, flashed the yellow card 11 times in what was a fairly tame game.
Ipswich hit the post as early as the second minute when Jon Walters took advantage of poor defending which blighted Argyle's whole afternoon to storm through.
More indecisiveness saw Garvan pounce on a mistake from Karl Duguid to open the scoring.
Argyle might have been given a chance to level when Rory Fallon was harshly judged to have been fouled by Gareth McAuley, clearly inside the penalty area, but Miller decided to award a free-kick on the edge of the penalty box.
Almost immediately, Ipswich doubled their lead when Garvan benefited from space given by Miller unintentionally blocking off an attempted tackle by Luke Summerfield to drive home Lisbie's pull-back from the edge of the box.
Ipswich sealed the three points within three minutes of the restart when Home Park old boy Norris forced Romain Larrieu into a save, with Lisbie, who had strayed offside earlier in the move, following up.
Cathcart, on loan to the Pilgrims from Manchester United, made the scoreline more respectable with his first senior goal when he headed home an 80th minute free-kick by substitute Craig Noone.