Scott Parker might have been very clear about where his priorities lie ahead of this FA Cup fourth round tie, but the Fulham boss can’t have been enamoured by this feeble display as his side were totally outplayed by a second-string Burnley side. The Clarets were in complete command from the off, with Jay Rodriguez ending a nineteen-match scoreless streak with a brace that put the game out of the Cottagers’ reach before Kevin Long ensured the scoreline more accurately reflected the visitors’ dominance with a late third.

Parker had spoken passionately in the week of growing up with the FA Cup but that Fulham’s perilous league predicament meant he would have to prioritise the two massive meetings with relegation rivals this week. Those games at Brighton and West Brom are arguably the acid test of whether his side, reshaped and competitive in the top flight as opposed to the cannon fodder that lost their first four fixtures, can mount a genuine survival bid. The manager’s call for fringe players to stake a claim for selection went unheeded as Burnley, carrying all the confidence that a win at Anfield provides, bossed the first half.

The only surprise was that it took Sean Dyche’s side half an hour to go in front. Michael Hector’s metamorphosis from the decisive figure who denied Cardiff with an incredible goal-saving tackle in last season’s play-offs to a doddery defender utterly devoid of confidence has been alarming and he endured an utterly miserable afternoon here. He could point to the heavy pitch, a consequence of the blanket of snow that covered west London this morning, as a reason for the untimely slip that would have allowed Matej Vydra to give Burnley an early lead save for an offside flag – but there was little mitigation for the rest of an error-strewn display.

The former Watford forward spurned a host of good chances to reward Burnley’s high-octane opening, miscuing wastefully wide after a speculative strike from Phil Bardsley had almost squirmed away from Marek Rodak. The Slovakian international did make a smart save to deny him moments later after Dwight McNeil had sent Vydra clear of a horribly square Fulham defence with a slide rule pass, but the hosts goal was leading a charmed life.

Their luck ran out just after the half hour mark when Jack Cork’s right-wing cross was gleefully glanced in by Rodriguez, who hadn’t scored since an equaliser against Liverpool way back in July. The one-time England international has happy memories of facing Fulham – having opened his Clarets account with a late winner against Whites in the League Cup in 2008 – and he was generously afforded the freedom of the penalty area by Hector to loop his header over a stranded Rodak.

Parker’s side, with eight changes from the team that had pushed Manchester United all the way in midweek, were passive and offered very little in the way of an attacking threat in the first period. Aleksandar Mitrovic could have done with his close range header not being ruled out for offside, but the Serbian still looks worrying short of his belligerent best, and neither he nor Aboubakar Kamara – paired together in a 3-5-2 formation that rarely troubled Burnley – offered Parker much of an incentive to start with them ahead of Ivan Cavaleiro on the south coast on Wednesday.

Fulham did at least start the second period at a far higher tempo with Joe Bryan’s raids down the left flank providing a sense of adventure that had been sorely lacking. The left wing-back came the closest to grabbing an equaliser being denied by a brilliant Bailey Peacock-Farrell save when an inviting cross from Bobby Decordova-Reid dropped onto his right foot. The Northern Ireland international reacted well to foil two follow-ups from Mitrovic at his near post, but rather than prompting a spell of Fulham pressure, the home side’s purposeful start petered out.

It was Burnley who looked the likelier to add another goal, although they were generously assisted by more calamitous Fulham defending. Ream lingered in possession thirty years from his own goal, was robbed by Vydra, who went too wide in trying to round Tosin Adarabioyo and Rodak, and Dale Stephens’ subsequent shot was blocked. But there was no escaping when a woeful piece of distribution from Ream allowed Vydra a clear run on the Fulham goal and Hector barged him unceremoniously to the floor. Rodriguez stroked the spot-kick down the centre of the goal and the away side had an unassailable lead.

A flurry of changes followed with Ruben Loftus-Cheek, impressive in the second half against Manchester United, producing a fine pass to set Kamara clear. The French forward was first denied by Peacock-Farrell’s fingertips before James Tarkowski got back to clear off the line just in time. Long added a third with nine minutes left, bundling home from inside the six-yard box after former Fulham trainee Johann Berg Gudmundsson had managed to kept a keep a lost cause alive. That commitment typified Burnley’s professionalism – and you have to worry about what impact this abject defeat will have on Fulham’s confidence heading into a pair of pivotal fixtures.

FULHAM (3-5-2): Rodak; Adarabioyo (Odoi 82), Hector, Ream; Decordova-Reid (Kebano 68), Lemina (Carvalho 82), Anguissa (Loftus-Cheek 68), Onomah; Kamara, Mitrovic. Subs (not used): Areola, Tete, Reed, Cavaleiro, Lookman.

BOOKED: Kamara.

BURNLEY (4-4-2): Peacock-Farrell; Bardsley, Pieters (Lowton 87), Tarkowski (Dunne 86), Long; Cork, Stephens, Gudmundsson, McNeil (Bensen 86); Rodriguez (Mumbongo 89), Vydra. Subs (not used): Norris, Mee, Brownhill, Westwood, Wood.

BOOKED: Tarkowski, Long.

GOALS: Rodriguez (31, pen 71), Long (81).

REFEREE: Andy Madley (West Yorkshire).

VIDEO ASSISTANT REFEREE: Chris Kavanagh (Lancashire).