They were poor in the first half and an unfortunate own-goal from Sean Raggett meant they were trailing at the break.
But they completely turned things around in the space of three minutes following the restart, courtesy of John Marquis’ penalty and a fine Tom Naylor finish.
The Blues were unable to become the first side to leave Devon with all three points, however, as Jerome Opoku hit an Argyle equaliser.
Kenny Jackett made one change from the side that had beaten Ipswich in the FA Cup nine days earlier.
Ben Close – who scored in Pompey’s last trip to Home Park – came in for Ronan Curtis, who was away on Republic of Ireland international duty.
Andy Cannon, Naylor and Raggett had all been doubts ahead of kick-off, but the trio were passed fit to feature.
There was also a welcome return to the bench for Jack Whatmough, who had been missing since the end of October with a hamstring injury.
It was battle between the sides with best home and away records in League One respectively, but the men from Devon made the brighter start.
Ryan Hardie raced onto a pass from Kell Watts and was able to beat Craig MacGillivray to the ball, only for the keeper to recover well and deny the striker.
Watts then did well at the other end to prevent dangerous deliveries from Ryan Williams and Callum Johnson reaching their intended targets.
But Plymouth broke the deadlock on 11 minutes, with Raggett the unfortunate man to be credited with the goal.
The defender had to try to stop Hardie converting Frank Nouble’s pass and could only tun the ball into his own net.
Pompey were seeing plenty of possession and getting into some dangerous areas, although a final key pass or shot proved elusive.
One good example was when Cannon showed some neat footwork to beat Panutche Camara and play a one-two with Marquis, but could not force his way past the last defender.
A sloppy pass from Rasmus Nicolaisen then allowed Camera to find Nouble, who found space and forced a fine stop from MacGillivray.
The Blues continued to push forward and try to find a route through the Arglye back-line, but Michael Cooper was not being forced into action.
Their best opening came in stoppage-time, with Williams not quite able to bring Cam Pring’s cross under control and seeing the ball bounce off him and fly wide.
Plymouth Argyle 1
Jackett made a double switch at the break, with Whatmough and Ellis Harrison on to replace Nicolaisen and Close.
But it was Plymouth who were first to threaten following the restart and they will be left wondering quite how the ball stayed out of the net.
MacGillivray got down to parry away Danny Mayor’s attempt and it seemed certain that Hardie would convert the loose ball, only for Pring to make a brilliant block.
Harrison then dived forward to try to meet Harness’ delivery from the right, but could not quite make contact.
And when the substitute was fouled by Tyrese Fornah, a Marquis free-kick cannoned back off the wall and the same players follow-up flashed past the post.
Then, when Williams’ cross was only partially cleared, a fierce Naylor strike had to be tipped over by Cooper.
But the Blues were level just past the hour mark when Watts battled with Whatmough to reach a cross and the ball struck his outstretched arm.
Referee Charles Breakspear had no choice but to point to the spot and MARQUIS confidently converted the penalty.
And the game was flipped on its head a few moments later when the Pilgrims defence failed to deal with Cannon’s cross.
The ball found NAYLOR on the edge of the box and the skipper expertly drilled it right into the bottom corner.
But it was then Plymouth’s turn to hit back on 78 minutes when they won a free-kick wide on the left.
MacGillivray was unable to claim George Cooper’s delivery, allowing Dom Telford to nod the ball back and leave Opoku with a simple finish.
With the game so delicately poised it was little surprise that tempers became frayed and both Naylor and Ben Reeves were booked for a spot of mutual shoving.
A knock from Williams then saw Haji Mnoga brought on for the final few minutes, which passed by without either side able to find a winner.
Plymouth (3-5-2): M.Cooper; Aimson, Opoku, Watts; Edwards (c), Camara (Reeves 84), Fornah (Grant 67), Mayor, G.Cooper; Nouble, Hardie (Telford 63)
Goals: Raggett 11 (og), Opoku 78
Booked: Opoku, Reeves
Subs not used: McCormick, Wootton, Canavan, Abraham
Pompey (4-2-3-1): MacGillivray; Johnson, Raggett, Nicolaisen (Whatmough 46), Pring; Naylor (c), Close (Harrison 46); Harness, Williams (Mnoga 90), Cannon; Marquis
Goals: Marquis 63 (pen), Naylor 65
Booked: Marquis, Cannon, Naylor
Subs not used: Bass, Downing, Morris, Hiwula
Referee: Charles Breakspear