Match ends, Fulham 0, Burnley 3.
Jay Rodriguez's double and a Kevin Long tap-in secured Burnley's progress to the fifth round of the FA Cup with a comfortable win over struggling Fulham.
The Clarets produced a dominant display and went ahead when Rodriguez headed home Jack Cork's cross on 31 minutes.
Rodriguez doubled their lead with a penalty after Matej Vydra was bowled over in the box, ending a 19-game goal drought.
Long netted Burnley's third as he poked home 10 minutes later.
Burnley will face Bournemouth or Crawley Town in the fifth round - the Cherries host Crawley on Tuesday, 26 January (19:00 GMT).
- Fulham v Burnley as it happened plus updates from the rest of the day's action
- Watch all the goals from the FA Cup fourth round
Vydra thought he had given the Clarets an early lead as he slipped the ball past Marek Rodak from 10 yards after Bobby Decordova-Reid gave possession away, but he was ruled offside by a late flag.
Aleksandar Mitrovic netted at the other end after Kamara flicked the ball up for him to head into an empty goal, but Kamara was offside from the original Decordova-Reid cross.
Burnley enjoyed the better of the chances in the first half, Vydra miscuing his shot from a Rodak spill and Johann Gudmundsson whistling an effort over the bar.
But Sean Dyche's side, who beat Liverpool at Anfield in the Premier League on Thursday, deservedly took the lead as Cork swung in a lovely cross from the right and Rodriguez stooped to head past Rodak and give the visitors a half-time lead.
Scott Parker's side enjoyed more of the ball in the second half but Burnley were in control and Bailey Peacock-Farrell's fingertip save was enough to deny Kamara a goal and protect Burnley's lead.
Vydra was brought down in the box and Rodriguez converted the penalty to score his second goal of the season, before chesting the ball down to allow centre-back Long to slot in from close range.
'Who knows how far we can go?' - what they said
Burnley boss Sean Dyche: "There were so many good performances from players who haven't played too much. I know they are good players but they remind you with displays like that.
"I'm shocked we got a penalty, I can't believe it! We average one every 24 games normally and that's two in a few days.
"We take each game as it comes, there are no guarantees. If we keep going as we have been lately who knows how far we can go? When everyone is fit I believe in all of them."
Fulham manager Scott Parker: "We didn't deserve a result today. It was a tough game and we couldn't match what we had to face today, we couldn't deal with them.
"I had to make changes because of the squad, we've got big games coming up so I don't regret that. That's the way it is.
"The focus is clear, I wanted to win today but now it turns on the league. We'll brush this one away and move on."
Rodriguez loves facing Fulham - the stats
- Burnley have beaten top-flight opponents away from home in the FA Cup for the first time since December 1999, when they defeated Derby County in the third round, while themselves in the third tier.
- Fulham have gone seven home matches without a win in all competitions for the first since 31 October 1995 (D3 L4).
- Fulham have lost four of their past five FA Cup matches at Craven Cottage (W1), as many defeats as in their previous 16 such fixtures there (W8 D4).
- Burnley's Rodriguez has netted in each of his past three appearances against Fulham in all competitions (four goals) - he hadn't scored in any competition since netting against Liverpool in July.
- Rodriguez was directly involved in three goals in a single game (two goals, one assist) for the first time since 26 December 2013 in the Premier League for Southampton v Cardiff (also two goals, one assist).
- 16TosinSubstituted forOdoiat 82'minutes
- 18LeminaSubstituted forCarvalhoat 82'minutes
- 14De Cordova-ReidSubstituted forKebanoat 68'minutes
- 29Zambo AnguissaSubstituted forLoftus-Cheekat 68'minutes
- 47KamaraBooked at 75mins
- 9MitrovicBooked at 86mins
- 5TarkowskiBooked at 75minsSubstituted forDunneat 86'minutes
- 23PietersBooked at 79minsSubstituted forLowtonat 87'minutes
- 11McNeilSubstituted forBensonat 86'minutes
- 19RodriguezSubstituted forMumbongoat 89'minutes
- Andy Madley
- Shots on Target
Second Half ends, Fulham 0, Burnley 3.
Offside, Fulham. Neeskens Kebano tries a through ball, but Denis Odoi is caught offside.
Corner, Fulham. Conceded by Kevin Long.
Substitution, Burnley. Joel Mumbongo replaces Jay Rodriguez.
Substitution, Burnley. Matthew Lowton replaces Erik Pieters.
Substitution, Burnley. Jimmy Dunne replaces James Tarkowski.
Substitution, Burnley. Josh Benson replaces Dwight McNeil.
Aleksandar Mitrovic (Fulham) is shown the yellow card.
Foul by Aleksandar Mitrovic (Fulham).
James Tarkowski (Burnley) wins a free kick in the defensive half.
Attempt blocked. Fabio Carvalho (Fulham) right footed shot from outside the box is blocked.
Substitution, Fulham. Fabio Carvalho replaces Mario Lemina.
Substitution, Fulham. Denis Odoi replaces Tosin Adarabioyo.
Goal! Fulham 0, Burnley 3. Kevin Long (Burnley) left footed shot from the centre of the box to the centre of the goal. Assisted by Jay Rodriguez following a set piece situation.
Foul by Neeskens Kebano (Fulham).
Dwight McNeil (Burnley) wins a free kick in the attacking half.
Erik Pieters (Burnley) is shown the yellow card for a bad foul.
Offside, Fulham. Ruben Loftus-Cheek tries a through ball, but Aboubakar Kamara is caught offside.
Attempt missed. James Tarkowski (Burnley) header from the centre of the box misses to the right. Assisted by Dwight McNeil with a cross following a set piece situation.
- All the goals, highlights and drama from Saturday's fourth-round ties are streaming now on BBC iPlayer