Wilfried Bony scored the winner as Swansea earned a morale-boosting 2-1 win over Wolves in the FA Cup.
It means Carlos Carvalhal's men join Cardiff and Newport in the fourth round, only the third time three Welsh teams have reached that stage in the competition's history.
Jordan Ayew opened the scoring in the third-round replay and although Wolves substitute Diogo Jota levelled the scores, Bony came up with the winner to ensure the home side secured a tie at League Two promotion contenders Notts County.
A low-key opening in front of a poor crowd saw Swansea move ahead early on.
Kortney Hause's slip saw Luciano Narsingh waste a fine chance when through on goal, but it mattered little as Ayew opened the scoring in the 11th minute.
It was a fine effort, the Ghanaian dancing his way through some static Wolves defending to slot the ball into the bottom corner and make it four goals in his last seven games.
Swansea midfielder Roque Mesa came close to making it 2-0, firing a volley wide as the hosts dominated the ball.
Runaway Championship leaders Wolves had disappointed, but they finally woke up in the latter stages of the half.
Alfred N'Diaye followed a booking with a shot blocked by Alfie Mawson, while at the other end Bony nearly created a goal for Connor Roberts who could not get the power required to finish.
In the driving rain, Wolves still turned around a goal down and Nuno Espirito Santo's frustrated touchline demeanour told the story of the first period.
The wet weather continued when the game resumed, the Liberty Stadium pitch cutting up and not helping the entertainment.
Both sides struggled to retain possession, Helder Costa firing over and then appealing in vain for a penalty for the visitors after falling in the box.
Nuno had seen enough and introduced Atletico Madrid loanee Jota from the bench with immediate dividends.
A Wolves breakaway fell to the Portuguese, he escaped down the left and put three Swansea defenders on the floor before finishing with ease. Home goalkeeper Kristoffer Nordfeldt should have come to collect and paid the price.
It looked like extra time may loom, but Swansea were back ahead within three minutes.
Tom Carroll's cross was not cleared by the Wolves defence and while those in orange stood still, Bony reacted quickest to poke the ball home and celebrate in front of the home fans.
It proved to be the game's vital goal as although Wolves pushed for an equaliser late on, Swansea held on for a win that will give the top-flight strugglers some much-needed confidence ahead of Monday's visit of Liverpool.