Millwall, welcoming back Kenny Jackett for the first time since his departure as boss after nearly six years in May 2013, looked dead and buried as Bakary Sako set up one and scored another to make it 3-0.
The 26-year-old helped Wolves get up and running after 23 minutes when Danny Batth volleyed home his corner before scoring with a free-kick after Ethan Ebanks-Landell made it 2-0 on the hour.
However Millwall had other ideas, and striker Lee Gregory gave the Lions hope three minutes later before Fuller netted twice in the last 10 minutes – although the drama was far from over.
Deep into eight minutes of stoppage time, Shaun Williams was sent off for Millwall after bringing down Lee Evans as the last man but Wolves could not capitalise with a free-kick and then a corner.
The Lions, winless in six before kick-off, had a quick start and forced Carl Ikeme to be quick off his line after just 70 seconds to cut out Alan Dunne’s long punt forward, which Gregory was bearing down upon.
At the other end, David Forde almost misjudged the bounce of Matt Doherty’s through ball with Sako in close attention.
The move eventually concluded with Matthew Briggs conceding a corner and from the set-piece Batth volleyed home at the far post.
Scott McDonald forced Ikeme into a low save a minute later and Jimmy Abdou then sliced well wide from 15 yards, having been teed up by Gregory.
Millwall had strong penalty claims turned down on 38 minutes when Gregory poked a loose ball away from Batth before appearing to be tripped by the defender.
Kevin McDonald whizzed a shot goalwards on the stroke of half-time but it was inadvertently diverted away from danger by his Wolves teammate Nouha Dicko.
Scott McDonald placed a free header against the post a minute later following a good burst forward and cross from Gregory.
But Wolves doubled their advantage just after the hour mark when James Henry’s free-kick deflected onto the post and Ebanks-Landell poked home from a yard out.
Sako extended the lead three minutes later when his exquisite free-kick flew past Forde and into the top corner.
Gregory made it three goals in six minutes when he touched possession away from Batth and slotted beyond Ikeme to pull one back for the hosts.
Fuller reduced the deficit further eight minutes from time when he hammered Scott McDonald’s knock back across Ikeme and into the net.
Fuller completed the comeback three minutes from time when he turned on the edge of box and fired powerfully beyond Ikeme.
Evans raced clear in the dying seconds and was brought down by Williams, who saw red, and Forde made a great save to deny Sako from the resulting set piece.