The Mariners, who dominated the first half, took the lead just before the break through Jon-Paul Pittman. There was some neat play between Jennings and East, before the ball eventually found the feet of Pittman in the box, who turned and hammered the ball past the Spireites keeper.
But the visitors came out for the second half with more fight and endevour and bagged a deserved equaliser on 64 minutes through Morrison.
And they were ahead on 71 minutes when some sloppy play by Town allowed Slew in to hammer the ball past Andy Warrington.
But Town weren't done, and a great ball from Antony Straker found the head of Marshall, directing the ball neatly past the Spireites keeper.
Jon Paul Pittman