They looked bright early on, but did not go ahead until the stroke of half-time when Enda Stevens was fouled and Matt Tubbs scored from the spot.
Gary Roberts was then brought down late on and stepped up to open his Blues account.
Gregg Wylde immediately reduced the deficit, but the visitors held on to leave the large army of travelling supporters feeling ecstatic.
Paul Cook reverted to the side that beat Dagenham in the league the previous Saturday.
That meant Brian Murphy, Christian Burgess, Stevens, Nigel Atangana, Michael Doyle, Roberts and Tubbs all returned after the midweek Capital One Cup triumph over Derby.
Pompey looked full of confidence following their back-to-back victories and came close to taking the lead in just the second minute.
Gareth Evans burst through the centre, only to be denied first by Plymouth keeper Luke McCormick and then skipper Curtis Nelson.
Kyle Bennett tried his luck from the edge of the box soon after, although McCormick was again equal to it, sticking up a hand to palm the ball over.
It was the Blues looking the more dominant side and Roberts met Evans’ cross with a volley that was deflected over.
The hosts did begin to apply some pressure towards the end of the half, however, and it took a fine save from Murphy to keep out Graham Carey’s fierce volley.
But the action was soon back up the other end and after Tubbs had swiped at thin air when well-placed inside the area, Atangana drilled a low effort straight at McCormick.
It looked the sides would be going in level at the break – however, there was still time for some late drama.
Referee Steve Martin pointed to the spot following a challenge by Hiram Boateng on Stevens and TUBBS stepped up to emphatically smash home the penalty.
Plymouth Argyle 0
It was the Blues who were first to threaten after the interval when Evans cut inside from the right and fizzed a shot narrowly wide.
And Tubbs also had an opportunity to grab his second of the afternoon, breaking into the box and flashing an effort past the post.
But the visitors were not looking as fluent as they had been before the break and were guilty of losing possession too easily.
Cook decided to make his first switch on 69 minutes as goalscorer Tubbs made way for Jayden Stockley up top.
The striker made an immediate impact – but not in a good way, as Martin showed him a yellow card for a challenge on Nelson.
Plymouth’s captain made way after being cut above his eye and replacement Ryan Brunt almost levelled, but could only turn Carey’s corner wide.
Another Carey set-piece was swung into the Blues box on 76 minutes and it was agonisingly out of reach for several of his team-mates.
Bennett saw his shot clear the crossbar at the other end as Pompey attempted to stem Plymouth’s attacking tide.
And Stockley came close to increasing the visitors’ lead when he met Roberts’ corner and was only denied by a good low McCormick save.
Victory did seem secure on 86 minutes, however, when Roberts burst into the box and was clumsily tripped by Gary Sawyer.
Martin pointed to the spot for the second time and, with Tubbs off the pitch, ROBERTS stepped up to hammer the ball into the bottom corner.
A stunning volleyed finish from Wylde ensured a nervy finale, but the Blues held on to secure all three points.
Plymouth (4-2-3-1): McCormick; Mellor, Nelson (c) (Brunt 72), Hartley, Sawyer; McHugh, Boateng; Tanner, Carey, Wylde; Reid
Goals: Wylde 89
Booked: Boateng, Mellor, Sawyer
Subs not used: Bittner, Purrington, Cox, Simpson, Bentley, Harvey
Pompey (4-2-3-1): Murphy; Davies, Burgess, Clarke, Stevens; Atangana (Hollands 71), Doyle (c); Evans, Roberts (McGurk 90), Bennett; Tubbs (Stockley 69)
Goals: Tubbs 45+2 (pen), Roberts 86 (pen)
Booked: Davies, Stockley, Hollands
Subs not used: Jones, Webster, Haunstrup, Chaplin
Referee: Steve Martin
Attendance: 11,476 (1,719 Pompey fans)