Ryan Hardie provided the only goal of a frenetic Devon encounter midway through the second half.
The Blues had rarely threatened up until that point and although they pushed forward late on, an equaliser was not forthcoming.
Danny Cowley made two changes from the side that drew on the road at Ipswich just a few days earlier.
Joe Morrell and Denver Hume both returned to the starting line-up, with Ryan Tunnicliffe and Clark Robertson dropping to the bench.
That saw Connor Ogilvie move back into the centre of defence, while Sean Raggett took the captain’s armband.
There was a familiar face in the opposition ranks, as former Pompey defender James Bolton was selected by the Pilgrims.
It was a contest full of intensity in the early stages, with the endeavour on the pitch matched by the passion in the stands.
But there was not too much to trouble either keeper, as the action all too often broke down once it reached the final third.
Joe Edwards missed a great opportunity by swiping at thin air after Danny Mayor and Panutche Camara had worked the ball to him.
The best chance came when Hardie slipped a pass across to Luke Jephcott, whose effort was well saved by Gavin Bazunu.
There was an opening at the other end when Ogilvie played the ball down the line for George Hirst, who cut inside and saw a shot blocked.
Pompey were able to keep the play alive, though, and a teasing low delivery from Hume was just out of reach for Ronan Curtis.
Mayor soon whipped a fine cross into the Blues area, although it somehow evaded everyone on its way out of play.
The midfielder then tried his luck with a long-range attempt that was spilled by Bazunu, but quickly gathered at the second attempt.
That was about it in terms of clear-cut chances, although there were a string of bookings before the break, including for Pompey duo Mahlon Romeo and Louis Thompson.
Plymouth Argyle 0
The breakthrough did not look like coming any time soon once the action restarted, with some patient play again not leading anywhere.
There was a neat one-two between Curtis and Hirst, but the former was crowded out when he burst into the box.
Jephcott then saw a couple of shots blocked in quick succession by Raggett and Hayden Carter before the play was halted because of a head injury for Hume.
Cooper was alert to the danger at the other end, as Aiden O’Brien tried to race onto a pass over the top from Carter.
But a heavy touch almost allowed Hirst to capitalise soon after, with the keeper just about doing enough to recover.
And the striker then tried to flick Ogilvie’s low cross into the net on the hour mark, only for Bolton to get in a vital block.
Plymouth began to apply some pressure and a couple of Edwards efforts from the edge of the box were blocked.
Cowley responded with his first change, as skipper Robertson came into the defence and Hume was withdrawn.
But the Blues soon found themselves behind, with Jordan Houghton stealing possession from Thompson and Camara squaring the ball for Hardie to fire home.
A double substitution soon followed as Pompey sought a way back into the contest, as Thompson and O’Brien made way for Tunnicliffe and Tyler Walker.
They both proved a lively presence for the visitors and a scramble in the box led to a shot for the former that was inadvertently diverted behind by team-mate Curtis.
There were certainly a few nerves starting to appear from the hosts and Hirst had a chance to level, only to glance a header wide from Ogilvie’s centre.
Green shirts were having to swarm around the area, as Pompey began to apply more and more pressure with the seconds ticking down.
Six minutes of stoppage-time provided added hope, although when Raggett sent a Tunnicliffe corner into the danger zone, the ball was turned wide by Curtis.
And the Pilgrims were able to see out a series of late corners to boost their promotion hopes and dent Pompey’s own play-off chances.
Plymouth (3-5-2): Cooper; Wilson, Bolton, Gillesphey; Edwards (c), Camara, Houghton, Mayor, Sessegnon (Law 86); Jephcott (Garrick 75), Hardie (Randell 90+4)
Goals: Hardie 65
Booked: Sessegnon, Cooper
Subs not used: Burton, Crichlow, Broom, Ennis
Pompey (3-4-3): Bazunu; Carter, Raggett (c), Ogilvie; Romeo, Morrell, Thompson (Tunnicliffe 71), Hume (Robertson 64); Curtis, Hirst, O’Brien (Walker 71)
Booked: Romeo, Thompson
Subs not used: Webber, Vincent, Jewitt-White, Mingi
Referee: Sam Purkiss
Attendance: 15,604 (1,381 Pompey fans)