Andrew Johnson and Liam Henderson notched their 21st and 13th goals of the season respectively to put the game to bed in the first half. Greg Hartley was in fine form in the Ashton goal to keep the scoreline respectable.
An even start to the game saw the visitors look to take the lead as Nathan Ntalu shot straight at Dan Lowson on 2 minutes.
On 13 minutes, Ryan Donaldson was denied by Hartley after the midfielder hit a swerving effort that was dipped over the bar.
The opening goal came on 31 minutes and it was Johnson who scored it. Receiving the ball close to the byline, he cut back infield before whipping the ball across the face of goal and into the back of the net.
Ashton had a great opportunity to level things up on 33 minutes but Ntalu shot tamely at Lowson.
At the other end Headerson, who was unmarked, saw a header clawed away by Hartley and just a few minutes later Johnson was also denied by the visiting keeper.
Liam Henderson eventually doubled the lead on 40 minutes as Jack Foalle crossed to the far post and Henderson threw himself at the ball to connect with a diving header.
Morpeth took control of the game as Ashton looked dejected and there was further chances before the interval with Foalle seeing an effort tipped over the bar and Henderson fizzing an effort narrowly wide.
Jeff Henderson was denied 30 seconds into the second half as Hartley clawed away a deft flick at the near post following a corner.
Johnson had another opportunity on 51 minutes when he got through on a one v one with Hartley but the ‘keeper did well to stand up and make the block as Johnson tried to round him.
Liam Henderson went close again on 71 minutes when Hartley turned aside his shot from a tight angle, whilst the closest Ashton went to scoring was in the 87th minute when Lowson pushed away a swerving Tom Bentham volley.
The Highwaymen are next in action on Saturday when they make the long trip to Derbyshire to face promotion chasing Matlock Town.