Peter Hartley struck deep into stoppage-time to condemn Pompey to another season in League Two.
The game seemed to be heading for an extra 30 minutes when the defender rose to head home a corner and break Blues hearts.
Both sides had earlier chances to score as the tie became increasingly ragged and open towards the end.
But it was Plymouth who were celebrating a 3-2 aggregate victory and trip to Wembley, while Pompey will have to go again in August.
Paul Cook stuck with the same side that drew 2-2 with Argyle in the first leg at Fratton Park.
The only change came on the bench, where a fit-again Conor Chaplin replaced his namesake Wilkinson.
Both sets of supporters at a warm and sunny Home Park were anticipating another exciting, incident-packed affair following Thursday night’s drama.
But, in reality, it was much cagier contest, with the sides unwilling to take too many risks in search of a goal.
It was the hosts who started brighter, though, and Ryan Allsop pushed Graham Carey’s shot over before Jake Jervis hit a free-kick off target.
But Pompey began to get a grip as the half progressed and the lively Kyle Bennett found the side netting after cutting into the box.
Marc McNulty then latched onto a long ball forward, only to roll a tame shot straight into the arms of Luke McCormick.
The visitors were starting to dominate possession, but were unable to cause the Argyle keeper any more problems.
Gary Roberts’ cute pass for Gareth Evans was cut out, while McNulty’s effort from distance sailed high over the bar.
Pompey received a blow on 31 minutes when Evans was caught by a strong challenge from Carl McHugh.
The Plymouth midfielder was booked by referee Paul Tierney and Evans limped off to be replaced by Adam McGurk.
And the replacement was soon involved in the action, first just failing to beat McCormick to Roberts’ clever pass and then teeing-up Bennett for a shot that was scuffed wide.
The Pilgrims were struggling to see much of the ball and when they did create an opening, Jervis wasted it.
Then, with the interval approaching, Cook was forced to make another substitution. This time it was Danny Hollands who went down, with Ben Close coming on in his place.
Half Time: Plymouth 0 (2) Pompey 0 (2)
Pompey were quickly out of the traps following the restart and after McNulty had bundled his way into the box, Roberts saw a shot deflected behind.
They then broke quickly up the pitch, with space opening up for the advancing McGurk, whose effort was comfortable for McCormick.
The visitors were starting to look a real threat and after Roberts was impeded 25 yards out, Ben Davies stepped up to curl a free-kick into the side netting.
It was Roberts who was next to have a go when McCormick raced from his box and made a poor clearance, but Pompey’s talisman could not steer the ball home.
Plymouth then enjoyed a decent spell of their own, with Jervis bending a shot past the post before Hiram Boateng steered Gregg Wylde’s low cross wide.
And they should have broken the deadlock on 58 minutes after McNulty over-ran the ball and Michael Doyle’s attempted clearance ricocheted into Jamille Matt’s path.
The striker bore down on goal, but went for power over accuracy and blazed his shot over the crossbar.
It was certainly more open than the first half and McGurk fired over after attempting to capitalise on a poor clearance.
And the action soon switched to the other end of the pitch, where Matt headed Carey’s corner wide from just a few yards out.
Pompey received another let off on 73 minutes when Carey’s header cannoned off Adam Barton and had to be cleared from the line by a well-placed McNulty.
They were struggling to keep hold of the ball, but did enjoy a spell of pressure late on, as Bennett beat a couple of challenges before seeing his shot deflected behind.
Plymouth could only partially clear the resulting corner and when the ball was sent back into the box, Close volleyed over.
But the hosts almost grabbed a winner on 89 minutes, only for an unmarked Jervis to head against the post after being picked out by Craig Tanner.
It was only a brief respite, however, as with just seconds remaining, Carey swung in a corner and Hartley arrived at the far post to head home.