Rolls Leisure showed why they were top of the Notts Senior League as they took the game to AFC in the opening 20 minutes.
Greg Conn on the right flank drew particular attention with his surging runs down the wing.
Jack James was also getting the better of the early exchanges in the middle of the park as a much changed AFC Mansfield struggled to get going.
Missing from the squad were Danny Naylor, Danny Tighe, Rockie White, James McCann, Joe Meehan, Julian Capuano and long term injury Joe Ward.
In came Craig Cantrell, back from injury, and three of the U19 squad, Declan Brewin, Ryan Fletcher and Brad Wilson.
Dean Rick’s first effort on 21 minutes signalled the visitors wake up call as it fizzed past the right hand post.
The striker went close again on the half-hour mark, but turned provider to open the scoring four minutes later.
Taking a Joe Naylor pass, his quick footwork set up Callum Gree,n who drove his effort in off the post from the edge of the box.
Naylor provided the pass on 40 minutes that produced the Bulls’ second goal, Rick racing into the box before rounding keeper Jake Pearson and firing home from six yards.
Pearson make a spectacular save to deny Green after good work from Rick on 42 minutes and the score remained 2-0 at the break.
It had been a miserable day to watch a football match and the rain got worse for the second half, but with AFC kicking up the slope there was still life in the game.
Mark Carter had two chances to extend the lead. Breaking into the box his first effort was sliced high and wide and his second bought another fine save from Pearson on 75 minutes.
Both teams had chances, but increasingly the visitors held possession. Nevertheless it took until the 81st minute for them to increase their lead, and it was leading goal-scorer Rick that provided the breakthrough.
After being denied a penalty minutes earlier for a surging run into the box, an identical run produced a different outcome as he was bought down by Aaron Smart. Rick dispatched the spot kick, sending Pearson the wrong way to make it 3-0 to the visitors.
A place in the next round was booked two minutes later when Rick bagged his hat-trick with a neat finish from Carter’s cross.
The Bulls will turn their attention to the FA Vase on Saturday as they fly the flag for the Mansfield area, being the only local side left in the competition, when they travel to Sileby Rangers in their first round proper tie.
Hucknall Rolls Leisure: Pearson, Paterson (Soloman 66), Marshall (Henrys 78), Matthews, Smart, Duncan, Conn, James, Start, Betteridge (Warden 30), Smith. Subs not used: Robinson, Wass.
AFC Mansfield: Sheppard, Cantrell (Brewin 78), McLane, Draper, Timons, Naylor J, Easom (Wilson 60), Buxton, Rick, Green, Carter. Subs not used: Fletcher, Rodger, Meehan.
Referee: Mark Tinsley.
Man of the Match: Dean Rick.
Elsewhere, Welbeck Welfare were knocked out 2-0 at home by Hucknall Town. Teversal beat Calverton MW 2-0, Clipstone saw off Kimberley MW 4-1 and Southwell City stormed through 7-0 against Ollerton Town.
In Windsor Foodservices Central Midlands League action, Kirkby Boys were 4-2 victors against Bentley Colliery in the Black Dragon North Division.