Ghana striker Jordan Ayew opened the scoring for Swansea with a beautiful goal.
He danced past a number of Wolves defenders before beating keeper Will Norris.
The visitors levelled through Diogo Jota midway through the second half, but Wilfried Bony quickly responded to seal a 2-1 win.
It was Ayew's fourth goal in his last seven games to set the Swansea on the path to the fourth round.
Watch Jordan Ayew's super finish after a virtuoso performance:
Jordan Ayew just scored this Worldie pic.twitter.com/f4EPeunUcp
— Thierry Nyann (@nyannthierry) January 17, 2018