Thursday's win came only a few hours after the former Burnley boss was sacked.
Eight goalless games in 10 outings, including just one shot on target in the previous 180 minutes, played a large part in Dyche's afternoon departure.
But more significant was the three league wins all season, leaving the team a point above the relegation zone. So with the manager gone, the third round of the FA Cup offered some respite in the hands of two club stalwarts - one the U18s coach and the other the long-serving captain.
However, their touchline stint will be a one-off with former boss David Moyes set to come back 12 years after leaving.
Beto's 42nd-minute strike, his third goal of the season coming in a third different competition, and Iliman Ndiaye's late penalty saw a team picked by Dyche before his departure edge past the 19th-placed Sky Bet League One visitors.
Seventeen-year-old academy graduate Harrison Armstrong, making only his sixth appearance, brilliantly threaded through a pass for Beto who had time and space to round goalkeeper Nicholas Bilokapic for a first goal since October.
Dyche's sacking came after days of negotiation over his pay-off on a contract due to expire in the summer and when the details were eventually finalised hours before kick-off, TFG pulled the trigger immediately.
The 53-year-old knew he was on borrowed time, having admitted to the owners his tenure had run its course after almost two years.
Fulham, meanwhile, had four different scorers as they beat Watford 4-1 in the third round of the competition at Craven Cottage.
After a well-worked counter-attack, Rodrigo Muniz scored his first goal of 2025 but Rocco Vata scored what will be considered a goal-of-the-competition contender with a thumping long-range effort to draw the sides level.
Raul Jimenez (49th minute) then continued his fine scoring record from the spot before Joachim Andersen (65th) and Timothy Castagne (85th) netted their first goals of the season to help Marco Silva's side topple his former club and advance.
At Bramall Lane, Cardiff turned the formbook around by dumping Premier league aspirants Sheffield United out of the competition.
Cian Ashford's 19th-minute goal was the difference between the second-division teams.
Sheffield are in third place in the Championship while relegation-threatened Cardiff are second from bottom - just three points above last-place Plymouth.
Sheffield were relegated from the Premier League in last place last season but are battling to bounce straight back up after 16 wins from their first 26 games this term.
Blades boss Chris Wilder said United, without injured on-loan Socceroos defender Harry Souttar, were "working tirelessly" to strengthen their squad.
"We've been talking the last 48 hours continually, working and trying to progress deals through," said Wilder. "It's a bit of a game of poker at times.
"But we've got players who want to come here, which is the biggest thing. And we've got owners and a chief exec who are working tirelessly to try and bring players in, which is good enough for me."