The Pompey talisman dispatched his spot-kick after Marc McNulty was fouled as a crackling clash finished 2-2.
McNulty had put Paul Cook’s side ahead early on before two Jamille Matt efforts turned the game on its head.
But Pompey were furious Matt was on the pitch to get his second after he stuck his head in on Michael Doyle.
An incensed Cook was sent to the stands after the incident – along with Pilgrims first-team coach Paul Wotton.
It proved a dramatic night worthy of the occasion as an enthralling tie swung backwards and forwards.
And no doubt there will be more twists and turns as the two League Two big hitters decide who will go to Wembley at Home Park on Sunday.
It was a blistering atmosphere at Fratton Park for kick-off.
And the roof was lifted off the Fratton end when McNulty broke the deadlock after three minutes.
Plymouth skipper Curtis Nelson lost the ball to Doyle and it dropped to the returning striker who blitzed a 20-yarder past Luke McCormick.
The lead lasted for six minutes as new loanee keeper Ryan Allsop failed to hold Gregg Wylde’s headed ball across goal and Matt bundled home.
There was a huge moment of controversy after 12 minutes when Matt appeared to put his head into Doyle who fell to the ground.
It looked a certain red card but referee Oliver Langford failed to spot the incident.
That incensed Cook who was then sent to the stands with Wotton as tempers boiled over.
The atmosphere was white hot and Pompey fans were feeling indignant when Matt doubled his side’s lead after 21 minutes.
A long throw into the box was held up by the Fleetwood loanee and he expertly lobbed the ball beyond Allsop with an overhead-kick.
Pompey were rattled and Graham Carey almost had a third for his side as he fired just wide from 30 yards.
Gareth Evans should have done better when well placed 10 yards out after 22 minutes but failed to get his shot off.
McNulty was inches away from levelling two minutes later when he fired wide from 20 yards after being freed by Roberts.
Kyle Bennett then saw his shot come back off the post from Ben Davies’ ball in as the frenetic action continued until the break.
Evans hit a shot just over the top from a charge forward two minutes after the restart.
And the Blues were level four minutes later as McNulty’s charge into the box was ended unfairly by Peter Hartley.
Roberts made no mistake as he stepped up and dispatched his effort high beyond McCormick’s dive.
The lively McNulty then charged forward and forced McCormick into a fine save with his 20-yard effort.
There was little doubt it was Pompey now in the ascendancy as the game ebbed back in their direction.
There were few clear chances, though, with Plymouth defending doggedly.
Evans fired over after a solo run and substitute Adam McGurk headed over from a corner with the minutes ticking down.
Davies forced McCormick into another stop at the near post late on before Evans’ acrobatic volley flew wide.
There was still time for Roberts to hit a late chance well wide of the mark.
But there was to be no dramatic winner as Fratton Park greeted the final whistle with applause on a night of play-off drama.