With 7 points from their opening three games, Kenny Jackett's side have been backed by many to push for an instant return to the Sky Bet Championship this season.
Wolves quickly set about living up to the tag of favourites too, with Kevin Doyle at the fore of their bright start. After just 7 minutes the Irishman pushed towards the byline inside the Crawley area and his excellent cross evaded the defence, allowing Bjorn Sigurdarson to head home his first goal of the season.
Undeterred by the early opener, Crawley were no pushovers, and were not overawed by their hosts. This, despite the fact that when they were promoted to the Football League three seasons ago, Wolves were still plying their trade in the Premier League.
Fast forward three years however and the sides have undergone extremely contrasting seasons, with Crawley giving more than a good account of themselves against their much-fancied hosts.
Their best opportunity to draw level came on 23 minutes. A delivery from the right created confusion in the Wolves area, and the ball eventually rebounded to an unmarked Joe Walsh just six yards out. Under heavy pressure from Danny Batth the chance still seemed easier to miss, but Walsh endeavoured to sidefoot the ball well wide with the goal gaping.
Crawley could easily have wilted after the early blow but they were unlucky not to be back on level terms by half-time.
Gary Alexander dragged a shot wide when well placed before the impressive Nicky Adams forced Wolves goalkeeper Carl Ikeme into a smart save.
Ikeme then saved from Adams and Clarke at the start of the second half as the Red Devils proved to be far from overawed in the lofty surroundings of Molineux.
Despite Crawley's best efforts, Wolves perhaps should have doubled their lead on 61 minutes when an excellent ball from the left found an unmarked Sigurdarson, but the striker couldn't quite reach the ball despite stretching.
The visitors applied some late pressure as they sought to avoid a second straight defeat in the league, and a deserved leveller was found after Jamie Proctor and Billy Clarke combined excellently, with the latter applying a great finish after 90 minutes.
Crawley appeared to be leaving the Midlands with a deserved point, but even more drama ensued after Kyle McFadzean was adjudged to have handled a cross from the left, with Leigh Griffiths scoring the penalty to break Crawley's hearts deep into injury time to send his side to the top of the league.