Hunmanby United earned a 4-0 home win against Seamer Sports to move level on points with Scarborough News Saturday League Division One leaders West Pier.
Ryan Baldry headed in the opener from a fine cross from Lee Micklethwaite on 30 minutes and then Cameron Dobson doubled United's lead on the stroke of half-time.
Dobson made sure of the win with his second on the hour mark and then unselfishly squared the ball when through on goal 10 minutes from time, allowing Olly Milner to net the fourth.
The whole United team shared their man of the match award, while Seamer boss Joe Wright admitted it was a below-par performance from his team.
Karl Storr's treble steered Whitby Fishermen to an 8-3 home win against Cayton.
Storr opened the scoring and further goals from Jordan Purvis and Storr made it 3-0 at the break.
Elliot Anderson, 16, made it 4-0 early in the second half, and then Alex May pulled a goal back for Cayton with a thumping 30-yard shot into the top corner.
Phil Spencer added a fifth, only for a rapid double from Cayton's man of the match Chris Weetman to give Mikey Dennis' team a glimmer of hope.
This was soon extinguished by the introduction of sub Mark Swales, who made it 6-3, then Storr completed his hat-trick before Swales struck once again.
Storr and central midfielder Anderson shared the man of the match award for Whitby.
Newlands booked their place in the last eight of the League Cup with a 5-0 home win against Sleights.
Centre-back Jordan Mintoft's acrobatic overhead kick after just two minutes put Newlands in front, while just before half-time Ben Luntley made it 2-0 after a fine run and lobbed effort.
Midway through the second half Drew McCoubrey made sure of the win with a fine solo goal and then the returning Matty Griffiths added a fourth just three minutes later.
Sub Jonny Manson completed the scoring with a cracking goal.
Teenage midfielder Liam Mancrief was man of the match for Newlands with fellow youngster Ellis Sellars also impressing.
Edgehill cruised into the quarter-finals with an 11-3 home win against Division Three side Goldsborough United.
Luke Jenkinson banged in five goals for Edgehill, with James Gunn and Joel Ramm netting a hat-trick apiece in what boss Steven Clegg called a poor all-round performance.
The United scorers were Tom Kilpatrick (2) and Simon Taylor.