Swansea looked like winning this match at a canter when they went 3-0 up after just 15 minutes through Andrea Orlandi, Joe Allen and Nathan Dyer. Orlandi’s strike was the fastest of the season, clocking in at just 24 seconds.
Steven Fletcher reduced the arrears but Danny Graham quickly made it 4-1 as both players ended their respective goal droughts. Wolves, for all their comical defending, looked increasingly dangerous in attack as the first-half wore on and Matthew Jarvis made it 4-2 after 33 minutes.
The already relegated visitors were the dominant team in the second-half of a thrilling encounter and David Edwards made it 4-3 before Jarvis completed a sensational comeback with his second goal of the game.
Swansea made two changes as Garry Monk and Orlandi came in to replace Angel Rangel and Neil Taylor. Orlandi featured on the left wing in a new 3-4-3 formation.
Terry Connor made two changes, with Christophe Berra coming in for the hamstrung Sebastien Bassong and Kevin Doyle replacing David Davis who had an eye injury.
Swansea took an early lead when Scott Sinclair crossed in from the left and Orlandi – impressing in a rare start on the left-wing - headed beyond Dorus De Vries.
It was quickly 2-0 as Allen, played in by Gylfi Sigurdsson, was given all the time in the world to stride through the gaping Wolves defence before seeing his shot deflect in off Richard Stearman.
Orlandi was catching the eye on the left and it was the Italian who weaved between two Wolves defenders before crossing for Dyer who headed in at the far post. Connor looked like he feared the worst on the touchline as he watched his defence being torn to shreds by Swansea’s vibrant attack.
Wolves, though, were the better team in the remainder of the first-half and Fletcher ended a run of nine games without a goal when he expertly headed Kevin Doyle’s left-wing cross beyond Michel Vorm and inside the far post.
But Swansea had not finished and Dyer teased and tormented the Wolves defence before crossing for Graham who controlled and rifled home.
Wolves continued to go forward at every chance and were rewarded for their sense of adventure when Jarvis scored the first of his two goals after 33 minutes.
Doyle crossed deep to the far post where the winger controlled and cut in before firing right-footed across goal and into the bottom corner.
A terrific run from Stephen Ward then resulted in Vorm having to parry his shot from the edge of the area before Graham went through one-on-one with De Vries at the other end. The former Swansea stopper kept his shot out and Wolves were able to clear their lines.
Swansea looked particularly vulnerable on the wings and manager Brendan Rodgers replaced the injured Orlandi with full-back Neil Taylor at half-time as he reverted to his usual formation.
The home side started the second-half well and almost extended the lead when Sigurdsson smashed the base of the post after connecting with a left-wing cross from Sinclair.
Moments later the Iceland midfielder forced De Vries to push his shot behind as the home side came out of the blocks the quicker in the second-half.
But the remainder of the game belonged to Wolves who showed the kind of enterprise and endeavour that has been so sorely lacking this season. Relegated after defeat to Manchester City last weekend, they played with freedom at the Liberty Stadium.
Rodgers's substitution did little to stem the tide and the impressive Edwards made it 4-3 when he slotted the ball into the bottom right corner after being played in by a cute ball from Michael Kightly.
Wolves continued to press and an incredible comeback was complete on 69 minutes.
Fletcher played a first-time ball across the area into Jarvis and the winger side-footed home.
The defending from both sides left much to be desired and Rodgers will be particularly concerned at how often his side were left exposed at the back.
Kightly spurned an excellent chance when he was played through by substitute Sylvan Ebanks-Blake only to sky the ball well over, while Luke Moore almost won it for the Swans in injury time.