Matt Doherty scored twice and then Ivan Cavaleiro hit the winner as Wolves broke Shrewsbury's hearts in an absorbing fourth-round English FA Cup replay at Molineux.
James Bolton's header and Josh Laurent's strike, after John Ruddy's error, had put the League One side 2-1 ahead. Doherty continued to taunt Shrewsbury, though, scoring twice in the first half having netted a late equaliser in the original tie.
Separated by 60 places, the visitors again threatened an upset but Cavaleiro's fourth goal of the season booked Wolves a trip to Bristol City.
It took the hosts just 78 seconds to open the scoring as they cashed in on sloppy Shrewsbury defending.
Morgan Gibbs-White's corner was returned to him and his delivery saw Romain Saiss get a touch before Doherty fired in from six yards. But after 11 minutes Shrewsbury stunned Molineux through Bolton's header from a corner before Ruddy let Laurent's drive slip through his hands for the second on 39 minutes.
Wolves benefited from another goalkeeping gaffe in first-half added time when Steve Arnold dropped a cross and Doherty nodded in.