That result denied the hosts going level on points with U21 Division leaders Jubilee Sports.
Luke Brammer and a Ben Talbot double gave Hillsborough the advantage as Alex Lindley and Aiden Hargreave replied for Dearne.
The hosts' day got worse with Luke Jackson sent off before the visitors wrapped up the points as Ivan Brown and Tom Lingard came off the bench to make the points safe.
Brunsmeer Athletic moved into the top half with a comfortable 7-2 home win over Chesterfield Town.
Brinsworth Whitehill recorded their first home win of season beating Beighton Falcons 2-1. Callum Doyle had given the hosts the lead before Beighton hit back to level through Luis Afonso-Ferreira.
A tight contest was settled when Tom Woolley climbed off the bench to hit the winner.
Swinton Athletic Spartans and Mosborough drew 2-2.
Elsewhere, there was plenty of drama in the U18 Division League Cup.
Sheffield FC Red, of Division Two, showed their higher divisional superiority as they booked their place in the third round with an 8-2 win over Division Three Parkgate.
Ablulkamil Barre, Jack Hackford and Mason Harmon-Siddall had Club leading 3-1 at the interval with just a Josh Taylor effort in reply.
Sheffield stepped up a gear in the second period running in five more goals through Daniel Kabeya, Esmond Tayki, Benefit Ndlovu, Hendrik Minvo and Hackford with his second of the tie.
Hallam Wisewood Black pulled off the day’s biggest surprise winning 4-2 away at Division One side Stocksbridge PS Blue, who had lost just once in their previous six league and cup outings.
Division Five leaders Sheffield Park Rangers must had quietly fancied their chances of a cup shock at home against Division One Handworth Ambers.
But the visitors had others ideas as they romped to a convincing 8-0 success.
Swallownest Blue were the highest scorers as they proved far too strong for Division Four opponents Brunsmeer Athletic, easing through 11-2. Alex Needham led the rout with a well taken hat-trick as Archie Goddard, Fraser Stenton and Jack Wood bagged a brace apiece. Joseph Milner and sub Ryan Coyle completed the scoring with Brunsmeer at least getting a couple of consolation goals through Guy Rosson and Connor Whelan.
Division Three leaders Sheffield United Junior Blades kept their hopes alive of a league and cup double with a 3-1 win over Sheffield North End of Division Four.
Jack Brear with a double and a Jacob Furness taking United’s unbeaten run to eight matches in all competitions.
Division Two Handsworth came out 5-3 winners in an entertaining contest with Porter Light Blue.