Luke Thompson opened the scoring for the hosts in the 13th minute, before Flynn McNaughton equalised just before the break.
A penalty from Tom Kennedy for Ramsbottom made it 2-1, before Nic Evangelinos extended the lead to 3-1 and a late goal from Iwan Heeley threatened a comeback.
Pickering Town remain bottom of the table with 11 points.
Workington, who remain at the top with 41 points, drew 2-2 at home with Trafford, with Conor Tinnion and Scott Allison scoring for the hosts, and Lewis Walters and Sam Baird for the visitors.
Elsewhere in the play-offs, third-placed Marine were involved in a six-goal thriller with a 3-3 result against Colne, while Pontefract Collieries and Tadcaster Albion drew 0-0.
Just five points separate teams from fourth to eighth, with Marske United defeating Brighouse Town 3-1 with goals from Kevin Burgess, Louis Johnson and Andrew Stephenson.
In eighth place, Runcorn Linnets continue their fine form in 2020 claiming three wins in three, with a 2-1 victory over Mossley.
Mossley broke the deadlock just before half-time, but Runcorn claimed the comeback with goals from Tom Owens and a successful penalty from Louis Corrigan in the second half.
Now in 11th place, City of Liverpool overtook their opponents in Prescot Cables in the league with a fine 3-0 victory, while Widnes defeated Droylsden 1-0.
Moving away from the relegation spot, Ossett United also claimed a 2-1 victory at home over Dunston, with two-first half goals from Andy Monkhouse and Tom Greaves enough to secure the points, despite a second half goal from Mark Fitzpatrick from the penalty spot.
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