A bright start to the second half helped AFC to a comfortable 3-0 win at the Moat Ground.
Gresley had numerous chances to find the back of the net but were denied by some resolute Bulls defending, before Jack Broadhead netted just in time for the break.
Jordan Annable and Ollie Fearon scored within just a minute of each other early in the second half, killing the tie off and securing a huge three points for the Bulls.
AFC were forced into changing their team just ten minutes before kick-off, as Jon D'Laryea replaced Mark Dudley who was injured in the warm-up.
Jason White's services were quickly called into action, brilliantly tipping Callum Riddell's curling effort out for a corner just three minutes in.
White was almost caught out 10 minutes later, coming out of his area to make a clearance, which fell kindly for Joseph Haines; his attempt to find the open net unintentionally fell to Lei Brown with just White to beat, but he couldn't grab a connection.
AFC's first chance came with 20 minutes played, as Jack Broadhead's volley went behind Ollie Fearon, who managed to connect with his heel but couldn't get the ball on target.
The hosts continued to press, and Liam Marsden had to throw in a last-ditch block to direct Haines' low cross onto the woodwork and out for a corner.
Not long after Fearon's flicked header bounced inches wide, Gresley stopper Ben Allsop had to bring out the best in his abilities to get down low and tip a header away in the style of Gordon Banks.
Perhaps against the run of play, AFC finally broke the deadlock just before the interval as Jack Broadhead flicked Liam Marsden's long throw into the far bottom corner with a precise header.
It could have been all square no more than a minute later, but Marsden produced a brilliant block to divert Kane Lee's effort away from just a few yards out after the striker rounded Jason White.
The second half saw a far less competitive game as AFC looked to establish a firm foothold and earned it just before the hour mark, thanks to Jordan Annable's effort bouncing over the goal line via the crossbar.
Just a minute later, the points were well and truly secured when Charlie Dawes' dinked ball fell nicely for Ollie Fearon, who rounded Allsop before poking home a quickfire third for the visitors.
Moatmen substitute Devante Reittie tried his hardest to change his side's fortunes, denied by the legs of Jason White whilst one-on-one before curling wide in a similar position just several minutes later.
It could have been four late on, but Liam Marsden blazed the ball over the crossbar after being fed through by substitute Jon Froggatt.
The win means that the Bulls can no longer be caught by bottom-of-the-table Gresley, whilst a draw for Carlton means Mark Ward's side are nine points clear of safety with just three games remaining.
Final score | Gresley 0-3 AFC Mansfield
Scorers | Broadhead (43'), Annable (59'), Fearon (60')
Gresley XI | Allsop, Steele, Branch (McKenzie 58'), Lawley, Smith, Sturgess, Haines, Lansdowne, Riddell, Lee (Reittie (46'), Brown
Unused substitutes | McIntosh, Deards, Weir-Dailley
Yellow cards | Lawley (49'), Brown (50')
Red cards | N/A
AFC Mansfield XI | White, Marsden, D'Laryea, Ghaichem (C), Lawrence, Annable, Dear, Buxton (Jumma 88'), Fearon (Wall 83'), Broadhead, Dawes (Froggatt 70')
Unused substitutes | Dudley, Crosby
Yellow cards | Lawrence (50')
Red cards | N/A
Man-of-the-Match | Jack Broadhead
Attendance | 163