The Clarets were dumped out of the cup in midweek by Championship side Bournemouth, but Dyche welcomed a plethora of first-teamers back to the fold for the trip to Selhurst Park, and it certainly paid off Johann Berg Gudmundsson, Jay Rodriguez and Matthew Lowton propelled Burnley to victory.
Dyche's side would have needed nothing short of a miracle to go all the way in the FA Cup, and while an early exit will dampen the spirits somewhat, they can simply focus all their efforts on their survival bid after they ended a three-game winless run in the Premier League with Saturday's win at Palace.
The hosts are now eight points clear of the dreaded bottom three after a marked improvement in results since the start of December, and as the team with the fewest goals conceded in the bottom half of the table (29), Dyche will now aim to build on the mere 17 that his side have amassed at the correct end of the pitch, as only Sheffield United (15) have struck fewer times so far.
Burnley would move 11 points above their 18th-placed opponents with a first home win of the month, but Fulham are not exactly short of confidence either and will be desperate to boost their own survival prospects when they make the journey to Turf Moor in midweek.
Josh Maja just has not been able to hack it at Bordeaux, but the striker has taken no time at all to get his Fulham career up and running with both goals in Sunday's impressive 2-0 win at Everton.
The triumph at Goodison Park marked the first time that Scott Parker had witnessed his side pick up all three points in the Premier League since November 30 - a run of 12 matches without a win in the top flight - but there is no question that the Cottagers have started to look more solid at the back over the past couple of months.
With only one defeat from their last five Premier League matches - with three clean sheets to boot in that run - Fulham are giving themselves a fighting chance of staying up, but an eight-point chasm currently separates them from safety, with multiple failures to convert draws into wins contributing to their position in the bottom three.
Nevertheless, Parker's men make the trip to Burnley with the knowledge that they are yet to taste defeat on the road in any competition since the turn of the year - winning two and drawing four - and 12 of the 19 top-flight goals that Fulham boast this season have come on unfamiliar territory.
However, Burnley have enjoyed an astonishing success rate in this fixture down the years, as Fulham are winless in 30 trips to Turf Moor (25 losses and five draws) since their last victory on the Clarets' turf back in April 1951, and Dyche's men crushed the capital outfit 3-0 in the FA Cup last month.
Burnley Premier League form: WWLLDW
Burnley form (all competitions): WLLDLW
Fulham Premier League form: LDDLDW
Fulham form (all competitions): LDDLDW
Burnley did not come away from Selhurst Park unscathed as Ben Mee and Erik Pieters both suffered injuries, and concussion protocols means that the former will not be available this weekend, while Pieters is touch and go.
Aleksandar Mitrovic's troubled campaign continued before the Everton game after he returned a positive coronavirus test, but Maja's spot up top is not under any threat after his brace against the Toffees.
Parker only has one absentee to contend with in the form of Tom Cairney, and the Fulham boss will be reluctant to shuffle the pack after such an impressive showing at Goodison Park.
Burnley possible starting lineup:
Pope; Lowton, Tarkowski, Long, Driscoll-Glennon; Gudmundsson, Cork, Westwood, McNeil; Barnes, Rodriguez
Fulham possible starting lineup:
Areola; Tete, Andersen, Adarabioyo, Aina; Reed, Lemina; Lookman, Loftus-Cheek, Decordova-Reid; Maja
We say: Burnley 1-1 Fulham
Both of these teams ought to be feeling good about themselves despite their precarious positions in the table, and this tie could easily go their way depending on which sets of attackers turn up on the day. Fulham have been relatively solid on their travels recently and the hosts are having to deal with fresh injury concerns, but we think Dyche's men will do enough for a point this week.