With a club-record 8-1 win in the FA Cup, Swansea offered further evidence of its revival under new manager Carlos Carvalhal on Tuesday.
Huddersfield was another winner in the fourth-round replays, beating second-tier Birmingham 4-1 after extra time to set up a last-16 meeting with Manchester United — three days after losing at Old Trafford in the Premier League.
Carvalhal has masterminded wins for Swansea over Liverpool and Arsenal in recent weeks to lift the Welsh club out of the Premier League's relegation zone.
Notts County, a team from England's fourth tier, provided a much easier test and Swansea took advantage by scoring four goals in each half at Liberty Stadium. The teams drew 1-1 in the original match last month.
"It's important if it's the best result in the (club's) history, but the most important thing is the attitude of the players that made all the difference," Carvalhal said. "I spoke to them before the game that we had a challenge."
Carvalhal played a team filled largely with fringe players and two of them — Tammy Abraham and Nathan Dyer — scored twice in the first half. Kyle Naughton, Wayne Routledge, Tom Carroll and debutant Daniel James added more goals after halftime to complete Swansea's biggest FA Cup win.
"I don't think they deserved to win 8-1 but it is one of those games where their finishing was Premier League standard," said Notts County manager Kevin Nolan, who played in England's top division for Bolton, Newcastle and West Ham.
The reward for Carvalhal is a meeting with the club that fired him in December, second-tier Sheffield Wednesday.
Huddersfield came from behind at St. Andrew's, needing an own-goal to take the game to extra time at 1-1. Steve Mounie, Rajiv van La Parra and Tom Ince scored in the extra 30 minutes as the northern club ultimately eased through.
Huddersfield may have lost at Old Trafford on Saturday, but David Wagner's side beat United at home in October.
In the other match Tuesday, third-tier Rochdale beat second-tier Millwall 1-0 and will play either Tottenham or fourth-tier Newport in the fifth round. Their replay is on Wednesday.
Steve Douglas is at www.twitter.com/sdouglas80