The prestigious competition is close to the heart of Wakefield boss Paul David, who scored in Emley's historic 2-1 defeat against West Ham United in the third round of the competition eight years ago.
But his side got off to the worst possible start on two minutes when Graeme Armstrong gave the visitors an early lead with a neat finish from a dangerous Dunston free-kick.
The College Grove club welcomed two new midweek signings to the side.
Greg Challender arrived from Goole to bolster the Wakefield midfield while former Worksop Town striker Demi Kyriacou partnered Steve Kenworthy in attack.
And the early setback didn't affect the hosts as they pushed into their opponents half for the equaliser.
Brighton Mugadza had the best chance but his long range effort was well blocked.
Dunston had their share of chances and had three penalty claims turned down by referee Foley.
Wakefield finally found the equaliser though Magadza when his neat footwork tricked two Dunston defenders before slotting the ball passed Andrew Clark in the visitor's goal.
The hosts went in to the break on level terms - for the first time this season.
But it didn't last for long as Bobby Scaife's men regained the lead five minutes into the second half when Graeme Armstrong broke the offside trap to slot home his second of the afternoon.
It didn't take long for Wakefield to respond though, and Mugadza levelled for the second time on 55 minutes as he turned the defender and smashed home a low drive from a dangerous free-kick to make it 2-2.
Paul David's men weren't prepared to go behind again and Steve Kenworthy and Simon Wright were working hard in the Wakefield attack to find the decisive goal.
And that finally came with 10 minutes remaining.
Kenworthy broke free of the Dunston defence to feed Mugadza whose inch-perfect cross found the head of new-singing Kyriacou who made it 3-2.
Wakefield could have put the tie to bed with a number of great opportunities in front of goal.
Marc Townsend had the best chance after being put through one-on-one with the keeper but his effort was well saved.
The one sour point of the afternoon was the sight of the industrious Simon Wright being stretchered off in the final minutes.
But Wakefield progress to the FA Cup First Qualifying round with their first victory of the season.