Despite their recent form Rangers started brightly with Bradley Grayson seeing his effort from the edge of the box saved.
Ashton goalkeeper Gregory Hartley was forced into another save on the 21st minute this time denying Jake Charles.
The Boro were rewarded for their efforts after 26 minutes with the opening goal for birthday boy Josh Green, who fired his free-kick home into the top corner.
Ashton replied after the break and Samuel Sheridan almost levelled the tie, but saw his effort picked out of the top corner by a fine save.
Ben Hardcastle was next to test the Boro goal, but saw his header fall just wide from an Louis Almond cross into the box.
The equaliser eventually came on 62 minutes with Josh Wilson heading home from a John Pritchard floated in cross.
Ashton struck the winner four minutes from time with Hardcastle’s cross met by Michael Brewster who flicked the ball home.