Having reached the FA Cup semi-finals three times in the first 110 years of their history, Crystal Palace have now done it for the third time in a decade, an impeccable away performance seeing them ease past a Fulham side that had much of the possession, did most of the attacking and achieved next to nothing.

With wonderful skill, Eberechi Eze scored one and created another as the visitors took control of the tie in four electric first-half minutes, before the substitute Eddie Nketiah sealed victory in the second.

Fulham v Crystal Palace: FA Cup quarter-final – live

For Fulham it was a fifth successive defeat at this stage of the competition, a downbeat end to a day they started in bright sunshine and high belief. The teams emerged to a cacophony of fans and flags and firework fog, the pre-match hype having the intended effect not just on the home supporters but on their team as Marco Silva’s side started the game like a swarm of wasps around a jam jar, all movement and excitement and danger.

It took them less than two minutes to create something, Rodrigo Muniz bustling past a couple of challenges and into the area before opening up his body and sidefooting towards the far post only for the ball to bend in the wrong direction and go harmlessly past the post.

But they could not sustain that energy, and Muniz in particular strayed from the combination of strength and perseverance with which he crafted that chance for himself. There was a period around the half-hour mark when within a couple of seconds of receiving the ball and almost irrespective of the circumstances he would invariably be on the ground, looking imploringly towards an unsympathetic referee.

It was from one such appeal that the opening goal arrived: Muniz grounded, Marc Guéhi gesticulating furiously behind him, the referee ignoring them both, the ball played quickly down Palace’s left flank. Tyrick Mitchell played infield to Eze, who cut inside Sasa Lukic and curled a deliciously precise shot inside the far post.

Jean-Philippe Mateta wore protection over his left ear in his first game back since he was badly injured by Millwall goalkeeper Liam Roberts in the fifth round. Photograph: Crystal Pix/MB Media/Getty Images

Four minutes later Palace’s lead was doubled, again from a swift attack down their left. This time Eze was released down the wing, tricked his way into enough space to curl a cross past Sander Berge and delivered the ball perfectly into the path of Ismaïla Sarr, who headed in at the near post. And for the first time, the home fans fell silent.

Home advantage never seems to count for much with these teams: in the league this season both encounters ended in 2-0 away wins, fresh affirmation of a long-term trend – not a single home victory in eight meetings this decade and just one in 12 across the last 20 years, a period in which precisely 20 goals had been scored by travelling sides and only nine by their hosts, before this latest addition to the canon.

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Fulham will feel they should have capitalised on their domination of the opening 20 minutes, even if for all the action and excitement they did not create another chance as good as the one Muniz missed in those early moments. Guéhi just beat Calvin Bassey to a header from a corner; Andreas Pereira sent a shot skidding wide after being found by Bassey’s pull-back. None of this did much to discomfit Dean Henderson in the Palace goal, and the spell was eventually broken in the 26th minute when, with the visitors’ first shot of any note, Jefferson Lerma sent a volley dipping over Bernd Leno and on to the crossbar.

The second half for Fulham was a similar story to the first, only with less precision and less hope. They dominated for a while and won a succession of corners, from which Palace won a succession of headers, before Henderson was finally tested by Willian’s 68th-minute curler, and again seconds later when the resulting corner, flicked on by Joachim Andersen, almost fell to Bassey.

Jean-Philippe Mateta made his widely predicted return after lacerating an ear in the fifth-round win over Millwall, nursing not just his injury but also a run of eight goals in his last 10 games. It was in many ways an ideal return, even if he may well have had fewer touches in this Cup tie than the 25 stitches with which he ended his last. He was taken off with 20 minutes to play and within five of them his replacement ended Fulham’s faint and fading hopes, Nketiah played onside by a dawdling Bassey as he ran into the left side of the area and sidefooting past Leno.