In a dramatic eight-goal thriller at the Liberty Stadium, the visitors came from behind to secure only their third point under Terry Connor following last week's relegation
Goals from Andrea Orlandi, Joe Allen and Nathan Dyer inside the opening quarter of an hour looked to have set the hosts on their way to an emphatic victory.
But the West Midlands’ outfit were primed to take advantage of some suspect defending from the Swans, with Matt Jarvis on target twice to earn the draw.
Brendan Rodgers made two changes to the side which drew 1-1 away to Bolton last weekend, with full backs Garry Monk and Andrea Orlandi coming into the side in place of Neil Taylor and Angel Rangel, with the latter dropping out of the squad completely.
Kevin Doyle was restored to the starting XI in place of David Davis for the away side, who missed out due to an eye injury, while Christophe Berra filled in at center back in place of the injured Sebastien Bassong.
The hosts got off to a flying start, with Wolves immediately sitting deep from the kick off to allow Swansea to indulge in their patient buildup way.
But not much patience was to be needed, with Scott Sinclair allowed time and space on the right-hand side to whip in a delightful cross that was nodded past goalkeeper Dorus de Vries by Orlandi to open the scoring within the first minute.
Just as it seemed things could not get much worse for the visitors, the Swans again played their way through the heart of the Wolves defense to double their lead.
Danny Graham did well to hold up the ball under pressure from Berra and find Gylfi Sigurdsson, who in turn played Allen through on goal, with the Welsh midfielder duly finding the back of the net, albeit due to a deflection off Richard Stearman.
Ten minutes later, Dyer poured more misery on Connor’s side with a headed-effort to put Swansea three goals to the good, with the brilliant Orlandi skipping past two defenders to assist.
After a scintillating start to the game, there was no let up, with Steven Fletcher rising to meet Kevin Doyle’s cross to pull one back for Wolves and kickstart a period of three goals in four minutes.
The Swans did not take conceding as a wake up call, as Dyer did well to work space before finding Graham, who controlled before firing past De Vries, only for Jarvis to cut in from the flank a minute later and settle the scores at 4-2 before halftime.
Just two minutes after the restart, Swansea again went close, this time Sigurdsson finding the base of the post from distance, but it would be Wolves who found the back of the net early in the second half, with Michael Kightly’s superb pass after Karl Henry’s quickly taken free kick allowing Dave Edwards to slot the ball past Michel Vorm.
The momentum firmly on their side, Connor’s men pushed for an equalizer, with Jarvis and Kightly threatening down the flanks and Fletcher just inches away from connecting with Berra’s cross, as the hosts were repeatedly forced into turning over possession.
But the visitors weren’t to be denied their fight back. This time Edwards played the ball into the path of Fletcher, whose first time ball found the run of Jarvis superbly to equalize from close-range and double his tally for the afternoon with 20 minutes remaining on the clock.
Kightly was presented with a late chance but he blazed his effort high and wide over the bar, as Wolves secured only their third point under Connor, but the manner in which it was sealed will mean it feels like much more.