The Swans saw anther three points snatched away from them late on as Damian Johnson secured a crucial draw for relegation-threatened Plymouth in controversial circumstances at Home Park.
Paulo Sousa's side looked to be heading for a vital victory in their quest for a play-off place after Darren Pratley fired them ahead at the start of the second-half with a superb strike.
But with just three minutes remaining, Argyle were awarded a late penalty after Andrea Orlandi handled Yala Bolasie's corner.
Jamie Mackie saw his penalty superbly saved by Dorus de Vries only for the linesman to signal that the Dutch 'keeper had moved. Referee Keith Hill ordered it to be retaken with Swansea furious.
Although Argyle changed their penalty taker, de Vries saved again from Damien Johnson only for the midfielder to follow up and fire the rebound home.
It was another cruel blow for the Swans after Newcastle snatched a late point at the Liberty last Saturday. Both were games Swansea deserved to win.
Plymouth: David Stockdale; Karl Duguid, Kari Arnason, Reda Johnson, Chris Barker (Joe Mason, 78'); Luke Summerfield (Yala Bolasie, 56'), Damien Johnson, Carl Fletcher (C), Chris Clark; Jamie Mackie, Rory Fallon (Kenny Cooper, 61'). Not Used: Romain Larrieu (GK), Bradley Wright-Phillips, Gary Sawyer, Alan Judge.
Swans:Dorus de Vries, Angel Rangel, Garry Monk(C), Alan Tate, Jazz Richards; Ashley Williams, Tom Butler (Mark Gower, 71'), Andrea Orlandi (Joe Allen, 84'), Darren Pratley; Gorka Pintado, Lee Trundle (Shefki Kuqi, 55'). Subs:David Cornell (GK), Nathan Dyer, Besian Idrizaj, David Cotterill.
Attendance: 9,185 Away: 742
Referee: K Hill (Hertfordshire)
Paulo made five changes to his side for the match at struggling Plymouth Argyle at Home Park.
It's all change in attack as Shefki Kuqi was replaced as the lone striker by the new pairing of Gorka Pintado and Lee Trundle, while Tom Butler came into the midfield.
There was a return to the defence for Angel Rangel and youngster Jazz Richards was also handed a start.
Swansea's new look side took to the Home Park turf and made an encouraging start to put pressure on the Argyle defence with a corner.
Andrea Orlandi's second minute delivery was easily collected by loanee 'keeper David Stockdale while he was also forced to stop Darren Pratley's by-line cross following fine work by Lee Trundle on the left-hand side.
Paulo's side were put under the cosh in the proceeding minutes as ex-Swan Rory Fallon sent a header into the hands of Dorus de Vries while the Dutchman collected two Kari Arnason long-throws into the box.
The best chances of the early moments of this game fell to Gorka Pintado, the striker twice forcing Stockdale into saving - the first with 11 minutes on the clock as he latched on to Trundle's through ball and again two minutes later when the goalkeeper did well to get down and deny him.
Damien Johnson saw his shot saved with 19 minutes on the clock but after that both sides failed to conjure up any attempts inside the final third as this game passed the half-hour mark.
There was a slight worry when Gorka Pintado went down after taking a stray arm to his face but following treatment on the sidelines was able to continue.
The Swans continued with their attempts to break down the Argyle defence with Darren Pratley in particular causing the home side problems down the right-hand side, but the home side did finish the half strongly.
A long-range half volley from Chris Barker was easily collected by de Vries on his line just before the break while Damien Johnson's attempt from 25-yards sailed high and wide right on the stroke of half-time.
Half-Time: Plymouth 0 Swans 0
The Swans made the best possible start to the second period as they broke the deadlock with just 40 seconds on the clock.
Angel Rangel played a low, pin-point through ball right down the middle of the park to pick out Darren Pratley running towards goal; the midfielder started his run from just inside the Argyle half and, as he reached the edge of the area, unleashed a powerful shot that found the bottom corner for him to register his sixth of the season.
Gorka Pintado flashed a header wide shortly afterwards and just before the hour the Rangel-Pratley combination struck again just before the hour with the defender playing in the midfielder to fire at goal from the angle, the shot on target only for Stockdale to do well and push it wide of the mark.
Sixty five minutes in and the new strike pairing of Pintado and Shefki Kuqi - who replaced Trundle early in the second-half - linked-up with the latter racing on to a chipped pass into the box only to be outmuscled by defender Reda Johnson.
Kuqi again failed to reach the ball ahead of Johnson who cleared Andrea Orlandi's cross away from the Finnish international's path but the home side came extremely close to levelling with a little over quarter of an hour remaining.
Jazz Richards was penalised for a foul on substitute striker Kenny Cooper on the right-hand touchline in line with the edge of the penalty area, the free-kick was cleared to Arnason and his effort from just inside the area was headed clear away from underneath the crossbar by AlanTate.
Plymouth were piling on the pressure as they went seeking a leveller and they were handed a glorious chance six minutes from the end when they were awarded a penalty.
Yala Bolasie's corner was handled by the jumping Andrea Orlandi which prompted Keith Hill to point to the spot.
Jamie Mackiesaw his penalty saved by Dorus de Vries, only for it to be retaken as the Dutchman was adjudged to be off his line. Argyle changed the taker, this time Damien Johnson stepped up and he saw his effort saved only to be successful with the follow-up.