It appeared as though the Blues were slipping to a fourth successive League One defeat after Ryan Hardie raced clear to score twice in the second half at Fratton Park.
That came after Lee Brown had doubled his tally for the season by converting a low free-kick for the hosts in the early stages.
Argyle were seemingly heading for the third tier summit, but Pompey kept pushing and were rewarded for their efforts with Raggett’s late contribution.
Danny Cowley made three changes from the side beaten by Cambridge – also on home soil – at the weekend.
Kieron Freeman, Joe Morrell and John Marquis all returned to the starting line-up, as Paul Downing, Miguel Azeez and Ellis Harrison dropped to the bench.
It meant a switch to a 3-4-1-2 system, with Freeman and Shaun Williams either side of Raggett at the back.
Ronan Curtis moved into a more advanced position alongside Marquis, while Marcus Harness floated in behind.
And the change had an instant impact, as the home side broke the deadlock with less than six minutes on the clock.
Conor Grant was booked for bringing down Mahlon Romeo just outside the box, although Pompey players felt the punishment should have been harsher.
Curtis shaped to shoot, but instead it was BROWN who took the free-kick, slotting it under the leaping wall and into the net.
There was a moving tribute to young Blues fan Sophie Fairall, who lost her brave battle with cancer earlier in the week.
Both sets of fans broke out into applause in the 10th minute, with all the players all stopping to join in.
There was then almost another goal when a low Romeo delivery was only cleared as far as Ryan Tunnicliffe.
He tried to sneak the ball inside the near post, but Mike Cooper got down to his left to push it behind.
The contest turned niggly as the first half developed, with referee Carl Brook dishing out a total of six bookings – three for either side – before the break.
Plymouth threatened themselves as the action progressed and Gavin Bazunu dealt with Luke Jephcott’s long-range effort.
Hardie then met Grant’s pass into the box with a neat flick that flashed a matter of inches past the post.
At the other end, Brown tried to repeat his earlier trick in stoppage-time, but this time slammed a free-kick straight into the wall.
Plymouth Aryle 0
The hosts were looking for a strong start to the second half, only to concede within three minutes of the restart.
It came from their own corner, with the ball hacked up the pitch and Freeman only able to head it into the path of Hardie.
The striker raced up the pitch with only the keeper to beat and neatly lifted home his shot to draw Argyle level.
There was a positive reaction from the Fratton faithful, who continued to get behind their side after that setback.
But the goal certainly seemed to knock the players off their stride, with a few sloppy passes seeing moves break down.
Plymouth were next to seriously threaten, with Bazunu off his line to deny Jephcott and the Blues then surviving a scramble in their box.
There was soon a chance at the other end, though, as Romeo’s effort was blocked by Ryan Broom, while Curtis could not get enough power on his header when the ball ran loose.
Romeo was looking particularly lively for the Blues and met Harness’ cross with a fierce volley that rattled the post, although he had strayed narrowly offside.
And they went close again moments later following some neat passing play involving Morrell and Harness.
The latter’s low centre was turned across the face of goal by Curtis, but a stretching Marquis could not guide the ball on target.
Both sides were looking capable of scoring a winner, with the action quickly switching from one end of the pitch to the other.
It was Plymouth who went ahead on 80 minutes, though, after Williams misjudged a Panutche Camara pass and Hardie broke clear to score his second of the night.
A gamble was needed and Freeman and Brown were sacrificed for forwards Reeco Hackett-Fairchild and Harrison.
But Argyle were using up whatever time they could to see out the closing stages – and it appeared they had done their job.
Then, in the final seconds of stoppage-time, Curtis swung in a fine cross that was nodded down by Harrison and RAGGETT turned the ball home from close range.
There was a mixture of relief and delight as Fratton Park erupted, with the final whistle sounding moments later.
Pompey (3-4-1-2): Bazunu; Freeman (Harrison 87), Raggett, Williams; Romeo, Tunnicliffe, Morrell, Brown (c) (Hackett-Fairchild 84); Harness; Curtis, Marquis
Goals: Brown 6, Raggett 90+5
Booked: Raggett, Curtis, Harness
Subs not used: Bass, Downing, Thompson, Azeez, Hirst
Plymouth (3-5-2): Cooper; Wilson, Scarr, Galloway; Edwards (c), Camara, Houghton, Broom (Law 85), Grant; Jephcott (Agard 90+2), Hardie (Garrick 87)
Goals: Hardie 48, 80
Booked: Grant, Edwards, Houghton
Subs not used: Burton, Gillesphey, Randell, Shirley
Referee: Carl Brook
Attendance: 13,375 (824 away fans)