Managers love a good whinge about fixture congestion and the excessive demands that it places on their players. To listen to some of them, it is as if the world of sport contains no greater evil. But here was proof that fatigue is as much a state of mind as of body.

Roy Hodgson picked a Fulham side with only two changes from the one that defeated West Bromwich Albion on Sunday. Yet the deeper into last night’s game that the Barclays Premier League team went and the closer to elimination from the FA Cup by lower-league opponents they came, the greater shone their energy, passion and determination. Instead of tiring, they grew stronger.

Swansea City were admirable for the first hour, but ultimately unable to resist the power of the momentum shift that occurred after they grabbed the lead early in the second half of this fifth-round replay. And so Fulham, for whom Bobby Zamora scored the winning goal in the 81st minute, will host Manchester United in the quarter-finals. That should really wear them out.

“People will envisage our demise,” Hodgson said. His team were crushed effortlessly at Old Trafford last week but have lost only once at Craven Cottage this season. “I’m sure we’ll give them a good game,” he said. “Of course we can beat them. We could beat Real Madrid or Barcelona. But are the odds on us winning greater than the odds on them winning? Pretty obviously, no. But they’ve got a lot on their minds. Maybe we won’t meet the Manchester United we met the other night.”

It was unexpected to meet virtually the same Fulham side who faced West Brom. With his team nestling comfortably in the unfamiliar surrounds of mid-table, Hodgson could afford the risks of refusing to rotate. Still, it is rare these days to see a manager treating this venerable competition with such respect. And Fulham’s next game is a testing trip to the Emirates Stadium to play Arsenal on Saturday. “I’m really surprised at the players’ energy levels, they were fantastic,” Hodgson said.

Yesterday marked two years to the day since Roberto Martínez took charge of Swansea at the age of 33. The Welsh club were promoted from Coca-Cola League One as champions last season and are only one point below the play-offs places in the Championship, but their beguiling style is as arresting as their results. “A good arrogance,” Martínez called it.

Neither manager disputed that Swansea had the better of the 1-1 draw at the Liberty Stadium, but their assessments of this game differed considerably. “I didn’t think there was any doubt about the outcome,” Hodgson said — a distinctly rose-tinted view.

“Over 180 minutes we deserved to go through,” Martínez said. “Until the first goal we were the better side. Probably we scored too early. Fulham should have been the side dominating from first to last, but we’ve got a great incentive to play in this sort of environment week in, week out.”

Fulham were caught cold less than 90 seconds into the second half when Mark Gower crossed for Jason Scotland, who prodded in his nineteenth goal of the season. The home team responded urgently and Swansea were put under sustained pressure. They were forced to prove that they are capable of desperate defending as well as delicate approach play, but the strain was intolerable and they cracked.

Clint Dempsey equalised from a corner by Simon Davies with 13 minutes remaining. Three minutes later, Davies crossed for Zamora to score his second goal in three days. Before Sunday, he had scored only twice all season. Unmarked, Zamora could hardly miss, and his downward header into the far corner was, unlike his manager’s team selection, perfectly orthodox.

Fulham (4-4-2): M Schwarzer — J Paintsil, A Hughes, B Hangeland, P Konchesky — S Davies, O Dacourt (sub: D Murphy, 60), D Etuhu, C Dempsey — R Zamora, E Nevland (sub: Z Gera, 60). Substitutes not used: P Zuberbühler, D Kamara, R Milsom, T Kallio, C Baird. Booked: Etuhu.

Swansea City (4-4-1-1): D de Vries — A Rangel, A Serran, A Williams, A Tate — N Dyer, J Gómez, L Britton, M Gower (sub: O Tudur-Jones, 55) — G Bauzà (sub: T Butler, 72) — J Scotland. Substitutes not used: D Cornell, K O’Leary, A Orlandi, F Bessone, M Collins. Booked: Bauzà.

Referee: M Halsey.