Chelsea cruised into the FA Cup semi-finals as Port Vale's storybook run was ended in ruthless fashion at Stamford Bridge.

Port Vale sit bottom of League One, 15 points from safety, but they reached the FA Cup last eight for the first time in 72 years by knocking out Premier League Sunderland.

This, however, was a brutal conclusion to their excellent campaign in the competition as Chelsea's multi-million-pound side ran riot against a team who started with eight free transfers and two loan players.

Chelsea ensured the notion of another giant-killing was extinguished swiftly, starting with a goal after 64 seconds when Jorrel Hato poked home from close range after Vale failed to clear a corner.

Vale, roared on by 6,000 raucous fans in the Shed End, initially responded well to that early shock, but the contest was effectively over in the 25th minute when Joao Pedro turned Kyle John in the area before beating keeper Joe Gauci.

Chelsea increased their lead three minutes before the break when Gauci pushed out Malo Gusto's cross and Cole Palmer's follow-up attempt went in off Jordan Lawrence-Gabriel.

It was then a question of damage limitation for Jon Brady's side, but that was beyond them too, as Tosin Adarabioyo headed Chelsea's fourth after 57 minutes from Malo Gusto's cross.

As Vale lost heart and hope, Andrey Santos added Chelsea's fifth with a far-post header from Estevao Willian's corner.

Estevao then got on the scoresheet himself eight minutes from time when he scored after Alejandro Garnacho hit the post, the goal being awarded after a lengthy video assistant referee check for offside.

Garnacho completed the rout from the penalty spot in stoppage time.

Chelsea's emphatic win was significant for head coach Liam Rosenior who can now prepare for a Wembley appearance after halting a run of four damaging defeats.

This game also followed the decision to impose a two-match suspension on Enzo Fernandez after the midfielder publicly questioned whether he would be at the club next season.

Following the final whistle, Rosenior responded to comments from Fernandez's agent, Javier Pastore, who said the Argentina World Cup winner did not understand Chelsea's decision.

"It is his opinion," Rosenior said. "I don't have anything to say on someone else's opinion. Enzo knows what I think of him. It was great to see him here and now we move forward.

"The conversations I have with my individual players stay within the dressing room. The dressing room is sacred."

Rosenior has been in an unforgiving spotlight, with Chelsea's string of defeats including a heavy Champions League loss to Paris St-Germain, along with a desperately disappointing display in their most recent Premier League game, a 3-0 defeat at Everton.

In the intervening period, Rosenior has had to deal with Fernandez and Marc Cucurella openly discussing a potential future away from Stamford Bridge.

Rosenior, therefore, was greatly relieved at the manner in which Chelsea produced a professional performance - denying Port Vale a fairytale Wembley trip and sparing him another headache.

He told BBC Sport: "It's great, it's why you come to this club, you want to win trophies, you want to be in big games and I was really happy with the players. Their attitude was top. We scored seven goals and that came from an energy and intensity which I enjoyed."

Chelsea's opening goal settled any nerves and tension that might have lingering from recent turbulence, and while Vale were stubborn for a while, once Joao Pedro added the second the game was as good as over.

Even Fernandez appeared in good spirits as he sat all smiles behind the Chelsea bench.

The star of the show for Chelsea was 18-year-old Brazilian Estevao, producing a bag of tricks, usually at high pace, that was too much for Vale to cope with.

He will be crucial as Chelsea chase silverware in the shape of the FA Cup, as well as a place in next season's Champions League through a lofty Premier League finish.

Rosenior said: "There is no ceiling for him. We've missed him. He comes in and just plays, he wants to get on the ball. Wherever he is on the pitch he's a threat."

This was as routine as any FA Cup quarter-final could be – and that will have suited Rosenior perfectly.

Port Vale's headline-grabbing run to this FA Cup quarter-final was ended in a painful manner as they were heavily beaten at Stamford Bridge.

As manager Brady put it, the final scoreline felt like a "gut punch".

But the visitors should take pride in their FA Cup run and the manner in which their supporters conducted themselves so superbly.

The look of despair on Brady's face as he turned away when Hato opened the scoring for Chelsea so early said it all.

Brady would have been hoping Vale could keep Chelsea at bay for long enough to allow nerves to build in the home team and among a fanbase that has registered its discontent during the recent poor run.

Instead, Chelsea and their fans were relaxed immediately, and for all Vale's early resilience, there was never any sense a shock was brewing.

Vale were over-run and outclassed – which was only to be expected given the gap in status and class between the two sides – but they never threw the towel in and gave everything until the final whistle.

Brady said: "We put ourselves under extreme pressure conceding in the first minute.

"Three set-pieces, we didn't defend well enough. Very frustrating. It shows in the end. To keep it at four or five would have been respectable, but to concede the last two was a bit of a gut punch.

"I'm proud of the players overall. It shows how ruthless the players are at this level and it's something we can stride to.

"It's a fantastic achievement what we did, the best FA Cup run [by Port Vale] since 1954. We beat a Premier League team and a Championship team in one week. We know our fate has probably been sealed to League Two and we have to come back fighting next year."

Vale's huge following never gave up on their side, providing deafening support throughout.

As Brady acknowledged, their battle against the drop into League Two looks destined to fail as they are in a parlous position, but this FA Cup run will have provided memories that offer at least some comfort.

Making light work of Port Vale is one thing, but next is a far tougher test for Chelsea who face their fellow FA Cup semi-finalists Manchester City on Sunday, 12 April (16:30 BST) in the Premier League.

Port Vale are swiftly back to League One duty, hosting Rotherham United on Tuesday, 7 April (19:45 BST).