The Highwaymen were three to the good by the 34th minute as Andrew Johnson bagged a brace, with Ben Ramsey notching his third goal for the club and Jack Foalle netting just after the break.
Morpeth dominated the early exchanges and the best of the chances came when they pulled their opponents apart down the right. Oliver freed Foalle and his low cross found Johnson on the stretch, but the forward couldn’t find a way past Daniel Lister.
Minutes later Johnson shot wide from the edge of the box.
The hosts hit the front through Johnson in the 19th minute, the forward cutting in and firing into the back of the net to provide the Highwaymen with a deserved opener.
That lead was doubled in the 22nd minute when Ramsey got in behind the defence and lashed into the bottom corner.
Two became three in the 34th minute as AJ registered his second of the night and 10th of the season. The forward slid in at the near post to score, converting Oliver’s low ball in from the right.
The second half started in similar fashion to the first, with Morpeth on the front foot and adding a fourth through Foalle. A lovely 52nd minute through ball released Ramsey down the left and he crossed for Foalle to slide in at the far post.
Jeff Henderson nodded wide from Ryan Donaldson’s cross on 61 minutes before his centre-half partner Michael Turner nodded wide from a corner.
Five minutes later and Ramsey got in behind again but drove straight at keeper Lister.
Liam Henderson went close on 78 minutes following a neat through ball by Donaldson. Clean through and with the keeper rushing out, he dinked past the stopper but the post too.
The game meandered to an already decided conclusion as Morpeth progressed in the Senior Cup to a home tie with Blyth Spartans.
The Highwaymen are next in action on Saturday when they host top of the table Matlock Town at Craik Park (3pm).