Boston Town suffered a third successive defeat to further hamper their promotion push.
This latest disappointing loss was their first at home in the league since October.
For the second week in a row, the Poachers took an early lead but fell away.
Jordan Nuttell struck after only two minutes to convert neatly from a Harry Limb cross.
But Gresley came back into the game and levelled ten minutes before half-time through Jude Ayetine.
The visitors netted twice more after the break through Haydn Brown and Jenson Cooper to seal the points.
Newcomer Shaun Archer had to fill in for the injured Luke Wilson in central defence and was named man of the match by match day sponsor Maintenance 4 Grassroots.
Boston Town remain second but will be desperate to returned to winning ways on Saturday (21 February) when they’re at home to Newark & Sherwood.
Kick-off is 3pm and the macyh day sponsors will be Tom Carter and family.
Town: Portas, Gibbons, Smith (Hudson), Priestley, Ford, Archer, Bayliss (Munton), Gurney, Nuttell, Limb, Cotton; unused subs: Henderson, Wilson
Boston Town FC 