Carlos Carvalhal can look forward to a reunion with the club he parted company with on Christmas Eve, only four days before pitching up in south Wales, after Swansea swept aside Notts County in emphatic style to stride into the last 16 of the FA Cup and set up an intriguing tie at Hillsborough on Saturday week.

Sheffield Wednesday’s loss is very much Swansea’s gain on the evidence of the last six weeks, with Carvalhal overseeing a run of only one defeat in 10 matches that now includes the club’s biggest-ever win at the Liberty Stadium. This rout is also Swansea’s record victory in the FA Cup and their highest domestic win since 1978, when Hartlepool were beaten 8-0.

It could not have been more comfortable for the Premier League club as they ran riot in front of goal on a night when Nathan Dyer and Tammy Abraham both scored twice. Kyle Naughton, Wayne Routledge, Tom Carroll and Daniel James, on his debut, were the other Swansea players to get on the scoresheet as this fourth-round replay rapidly turned into an exercise in damage limitation for Notts County.

Unfortunately for Kevin Nolan and his players, Swansea were not particularly forgiving in that respect as they cut through Notts County time and again. Dyer’s goals were his first since he scored for Leicester against Aston Villa in September 2015, in their title-winning season, while Abraham registered for the first time since October.

Although avoiding relegation, rather than trying to reach an FA Cup final, remains Swansea’s priority this season, Carvalhal was entitled to take plenty of encouragement from not just a fourth successive home victory – something they have not achieved since May 2016 – but also the professional and ruthless way that his players set about the task of dispatching lower league opponents.

Luciano Narsingh celebrates Swansea’s third goal against Notts County with Nathan Dyer, who was on the scoresheet for the first time since 2015. Photograph: Matthew Childs/Action Images via Reuters

“I am very proud of my players,” Carvalhal said. “I talked with them before the game and said that playing with high motivation against Liverpool, Arsenal and Tottenham is normal. Our challenge is to motivate the players against teams below. I said to them to show to everybody how much they wanted to win. Notts County are not a weak team. They are a good side, they put Brentford out of the FA Cup away. But tonight we played this game like we did against Liverpool and Arsenal. The attitude was very good and the dynamic very high.”

As for going back to Sheffield Wednesday, Carvalhal made it sound like he could not wait to be reunited with the club he left by mutual consenta little more than six weeks ago. “I feel that I will be back home,” he said. “That was my home for two seasons and a half and I was very happy there. I am an Owl forever and I have a fantastic relationship with the chairman. He’s a friend to me.”

For Notts County, who are third in League Two and chasing promotion, it was a chastening evening in many respects. Their travelling supporters were magnificent, however, and they deserved to see Noor Husin score a lovely goal to make it 3-1. “We need to take this hit and keep smiling,” Nolan said.

Abraham opened the scoring when he turned in Narsingh’s cross at the near post and then turned provider 83 seconds later to put Dyer clean through. The winger beat Adam Collin, the Notts County goalkeeper, with the minimum of fuss and then swept home his second and Swansea’s third with a terrific first-time shot from Narsingh’s pass.

Although Husin’s curling left-footed effort briefly pegged back Swansea, normal service resumed just before the interval when Abraham confidently dispatched another Narsingh cut-back. Swansea were rampant and it soon became clear there would be no let up in the second half. Naughton punished Collin’s poor punch and volleyed home to make it 5-1 and there was still more than half an hour remaining when Routledge, cutting inside before placing a low shot into the corner, racked up Swansea’s sixth.

Carroll, with an exquisite curling shot into the top corner, added the seventh and it was a special moment for James, the 20-year-old substitute, when he scored the final goal after some good work from Abraham, who has lost his way a little since that England callup back in November. “He’s progressing, but he knows that he can do better,” added Carvalhal at the end of a highly satisfactory evening.