Mick McCarthyâ€™s men were completely outplayed for most of the encounter but managed to score twice late after the visitors netted two goals in the first half to move to eight points as Swansea went to nine.
Swansea hit the lead in the 23rd minute when Danny Graham scored his third in three matches thanks to Mark Gowerâ€™s chipped through ball which evaded an acrobatic Roger Johnson and fell nicely for the former Watford man who coolly slotted underneath Wayne Hennessey to make it 1-0.
Just over ten minutes later, Graham turned provider when he ran onto a long ball from Angel Rangel before advancing to the edge of the area on the right and then producing a perfect low cross for Joe Allen to tuck away for his first Premier League goal, much to the dismay of the frustrated Wolves fans.
After failing to trouble Swans keeper Michel Vorm for most of the 90 minutes, Wolves hit back with just over five remaining when a corner was not cleared properly and Sam Vokesâ€™ initial shot was kept out but only as far as Kevin Doyle who tapped home with ease.
And the home side then completed a great fightback when Doyle took it down the left and cut back for Jamie Oâ€™Hara who hammered it into the back of the net with his right foot to send the Molineux fans into hysterics.
The overall performance of Wolves, who had lost their previous five matches, would have been unacceptable for McCarthy but the fact they showed resilience and courage to take a point against the odds would please him to no end whilst Swanseaâ€™s Brendan Rodgers would certainly be ruing the fact his side did not finish their opponents off earlier for their first away win in the Premier League.
TRIBAL ASKS: Are these two teams capable of finishing in the top half or will they be battling relegation come seasons end?
Yellow cards: WOL - Richard Stearman 47â€™, Jamie Oâ€™Hara 66â€™
SWA - nil