The Swans grabbed their first away point in the Premier League, but they threw away a 2-0 lead at Wolves.
Two goals in two minutes from Kevin Doyle and Jamie O'Hara salvaged a point for Wolves, who really should have been out of the contest going into the final seven minutes.
Danny Graham had put the Swans ahead in the first half and he set up Joe Allen to ensure the Swans went into the break 2-0 up.
Scott Sinclair went close on a a number of occasions in the second half in a contest which looked like going only one way.
But Wolves stunned the visitors with their late onslaught, and the hosts went close to pinching the game in the dying moments through sub Nenad Milijas.
Swans boss Brendan Rodgers made just one change to the starting XI which lost at Norwich City.
Mark Gower&nbsp;was restored to the starting line-up with Wayne Routledge dropping to the bench. Garry Monk led the side with Greece international Vangelis Moras on the bench.
Ex-Swans stopper Dorus de Vries was still waiting to make his first Premier League appearance for Wolves, and he was among the replacements for the game against his former club.
Wolves: Wayne Hennessey, Richard Stearman, Karl Henry, Sylvan Ebanks-Blake (Sam Vokes, 83), Stephen Ward, Roger Johnson (capt), Christophe Berra, Matt Jarvis (Adlene Guedioura, 67), Adam Hammill (Nenad Milijas, 67), Jamie O'Hara, Kevin Doyle.
Subs: Jody Craddock, Stephen Hunt, Matt Doherty, Dorus de Vries.
Swans: Michel Vorm, Angel Rangel, Ashley Williams, Garry Monk (capt), Neil Taylor, Mark Gower (Vangelis Moras, 85), Leon Britton (Andrea Orlandi, 74), Joe Allen, Nathan Dyer (Wayne Routledge, 83), Scott Sinclair, Danny Graham.
Subs: Gerhard Tremmel, Jazz Richards, Luke Moore, Leroy Lita.
Referee: M. Oliver
With both sides looking to make a good start, the game got off to a flying start.
Wolves tested Michel Vorm within the opening 60 seconds as Garry Monk's header from Richard Johnson's long ball fell to Karl Henry, who connected with a fine half volley. Vorm spilled the powerful effort, but the Swans managed to clear the danger.
The Swans replied via Nathan Dyer, who outpaced Stephen Ward and fired in a low shot which Johnson deflected for a corner.
Then it was the turn of Joe Allen to probe. He struck a sweet right-footed shot from 20 yards which Wales team-mate Wayne Hennessey tipped over for corner.
The Swans pushed again, this time Angel Rangel's cross was volleyed wide by Danny Graham at full stretch.
After a passage of Swans pressure, Wolves fought back. Matt Jarvis saw his effort on the penalty spot blocked by Angel Rangel before Jamie O'Hara's powerful drive was kept out by Vorm.
However, with 24 minutes on the clock, the Swans found the break through. Mark Gower's fine chipped pass caught Johnson wrong-footed, and Danny Graham had time to pick his corner and slot past Hennessey from eight yards out.
It was Graham's third goal in as many games, and the striker was certainly looking confident.
Things got a lot better ten minutes later. A sublime chipped pass from Rangel caught the Wolves defence flat-footed and Graham raced away down the right flank. His perfectly-timed low cross found Allen, and he side-footed past Hennessey to double the lead.
Jeers came from the home crowd, cheers were flowing from the away end.
The jeers almost got louder as Sinclair's half-volley was parried with Hennessey and the keeper's attempted clearance cannoned off Graham and bounced just wide of the post.
It was pulsating stuff - for the away team anyway - and the Swans deservedly headed into the break with a 2-0 lead.
Half-time: Wolves 0 Swans 2
Wolves were looking to make an immediate impact after the break, but the Swans were looking solid throughout.
Jarvis headed wide from Hammill's curling cross, then Rangel blocked efforts from O'Hara and Jarvis seconds apart.
The Swans were not going to sit on their lead, though, and Sinclair almost made it 3-0 after he got on the end of Gower's excellent cross. Hennessey, however, was up to the task and snuffed out the effort for a corner.
The winger was at it again soon after as he broke forward into the box but he lost his footing at the key moment.
Sinclair went even closer to getting his third of the season as he tested the defence again by cutting inside and shooting. His effort deflected off Johnson and over Hennessey, but dropped onto the top netting.
Wolves boss Mick McCarthy then made a double change with Nenad Milijas and Adlene Guedioura replacing Adam Hammill and Jarvis.
He was looking for a reaction from his side, but it was the visitors who went closest to grabbing the all important third goal.
Brendan responded by handing Andrea Orlandi his first Premier League appearance with 15 minutes left as he took the field in place of the excellent Leon Britton.
It was still the visitors who looked more likely to get the next goal, with Gower seeing his chip back into the middle deflect off Johnson and into Hennessey's hands.
McCarthy made his last roll of the dice by throwing on Wales international Sam Vokes in place of Sylvan Ebanks-Blake, while Wayne Routledge replaced Dyer for the last seven minutes.
Then, out of the blue, Wolves grabbed themselves a lifeline.
From a corner, Johnson's shot on the turn was kept out by Vorm but Doyle fired in from six yards.
Brendan responded by handing Vangelis Moras his first appearance in place of Gower as the visitors put an extra body in at the back.
Then, Molineux erupted with four minutes left.
O'Hara got onto the end of a cut-back pass and blasted high into the net with a powerful effort.
Suddenly, the Swans were desperately holding on for a point.
Milijas went within inches of grabbing a winner as his effort bounced just wide, while Moras made a crucial header in his own box.
That was it for a pulsating encounter, though, as the Swans somehow ended up with just a point.
It was the club's first point on the road in the Premier League, but it certainly felt like two points lost.