Bradley Wright-Phillips and sub Joe Mason netted the goals either side of the interval, while Argyle keeper David Stockdale pulled off a string of fine stops to deny the hosts who tamely surrendered their 14-game unbeaten home run.
Argyle were the first to threaten with Wright-Phillips firing wide from 20 yards before Daryl Murphy volleyed over for Town after Gareth McAuley had nodded down a Damien Delaney free-kick.
Murphy shot into the side-netting from a Jack Colback pass and Brian Murphy then dived well to turn aside a fierce low drive from Wright-Phillips as both teams continued to create chances.
Ipswich enjoyed a decent spell of pressure with Pablo Counago and Colback volleying over and McAuley heading wide but their best first-half chance fell to skipper Jon Walters who put a free header across goal from Carlos Edwards' excellent cross.
Against the run of play, Plymouth went ahead when Jamie Mackie robbed the dawdling Delaney, Carl Fletcher swept the loose ball wide to Yannick Bolasie who beat David Norris and fired over a cross for the unmarked Wright-Phillips to head home from eight yards.
Town had the ball in the net just before half-time when McAuley bundled in at the far post after Counago and Walters had helped on a David Wright long ball, but the flag was correctly up for offside.
After the break, Mackie was first to threaten with an angled drive wide before Counago forced a good diving save from Stockdale, with Edwards rifling the loose ball into the side-netting from a tight angle.
Stockdale pulled off another fine save soon after, turning away McAuley's downward header from another fine Edwards cross, before he made an easier stop to deny Walters' deflected drive.
Bolasie shot into the side-netting for Plymouth on a breakaway before Stockdale made another good save to deny Daryl Murphy who had got in behind the visiting defence onto a fine pass from Counago.
Brian Murphy made a good save to parry away a firm Bolasie header after he was picked out by fellow wideman Chris Clark and soon after Ipswich made their third substitution - David Healy joining earlier replacements Owen Garvan and Grant Leadbitter.
Garvan dragged one effort wide before Leadbitter's curling free-kick brought a brilliant diving save out of Stockdale, but Garvan then had a telling impact at the other end of the field.
His attempted header back to his goalkeeper was well short and collected by Mackie, and although McAuley got back to make a fine challenge on the striker, the loose ball was prodded home by Mason.
There was still time for Stockdale to make another brilliant save to turn away Healy's close-range header, but Plymouth held on comfortably for three crucial points, while Town know they still need a few more for safety.