Danny Rose hit a brace as Stags booked their passage into the next round of the cup with a 3-1 win at Shaw Lane.
Stags had been level at the break before their class shone through.
Krystian Pearce had earlier given the visitors the lead at the home of the Northern Premier League outfit.
Lee Bennett ensured parity at the break, before Rose ended any hopes of a huge scalp for the hosts – placed 58 places lower in the football pyramid.
Jacob Mellis had a penalty thwarted by Jon Stewart, who had a decent game despite the scoreline.
The Stags dominated possession, but it took 34 minutes to break down the Ducks.