The district will have four representatives in the third round of the North Riding Saturday Challenge Cup thanks to dominant performances on Saturday.
Harry Beresford got two in Richmond Town Reserves’ 5-1 win at home to Yarm and Eaglescliffe Reserves.
Also getting on the scoresheet were Ross Gladman, Joe Ramsay and Tyler Spence.
Unicorn had a tougher game against Sporting Knavesmire, who are unbeaten in the fourth division of the York Minster Engineering League.
But goals from Nigel Cole, Tom Keegan and Liam Reeves were enough to see the Richmond team through.
Richmond Mavericks progressed more comfortably with an 8-1 win over Union Rovers of the Beckett League.
James Kelly continued his good form with four goals, while Sam Pickersgill got two.
Brandon Gredziak and Zak Cleminson also netted.
Catterick Garrison went through thanks to a walkover win over Wombleton Wanderers.
Back in the Scotts 4 Storage Wensleydale League, Spennithorne came from behind to beat Hawes 2-1.
Tom Calvert scored after 19 minutes for the upper Dales men, but second half goals from Lee Thompson and Kalem Stanger secured the three points for Spenni.
Elsewhere, Carperby cruised to a 6-0 home win over Reeth.
Tim Weatherill opening the scoring after a great cross from Michael Dent.
Dent then headed in the second from a Paul Stephenson corner. Sam Lambert put the hosts firmly in control when he followed in to score from close range.
The fourth came from James Metcalfe when he got on the end of a Stephenson free kick. Carperby got their fifth before half time after good work from Sam Lambert and Tim Weatherill put Michael Dent in who finished well to smash the ball past the on coming Reeth keeper.
Carperby had most of the play in the second half, and missed a number of chances before centre back Dave Fullerton scored the goal of the game with a half volley on his less favoured right foot.
Carperby 6-0 Reeth
Spennithorne 2-1 Hawes
Richmond Town Reserves 5-1 Yarm and Eaglescliffe Reserves
Unicorn 3-1 Sporting Knavesmire
Union Rovers 1-8 Richmond Mavericks
Catterick Garrison v Hawes
Richmond Town Reserves v Reeth
Spennithorne V Richmond Mavericks
Unicorn v Carperby