The Stags pulled off a shock 1-0 away win at Sunderland's Stadium of Light on Saturday for a second successive season to ensure they were in the hat.
Rhys Oates was the hero with the early winning goal to delight the 1,300 travelling fans.
It was the first time all season Nigel Clough's men had produced back to back wins, after enduring a 14-game run without a victory.
Now they await the second round draw which could produce possible local derbies against the likes of Chesterfield, giantkillers Buxton and Notts County, if the Magpies can win their replay against Halifax.
Supporters can watch the draw live tonight on ITV4 at the end of the Dagenham & Redbridge v Salford City tie, around 9.30pm.
Ties in the second round will take place across the weekend of Friday, 3rd December 3until Monday, 6th December, with the 20 winning clubs collecting £34,000 each from the competition prize fund.
Full ball numbers
1. Bradford City or Exeter City
2. Mansfield Town
3. Sutton United
4. Sheffield Wednesday or Plymouth Argyle
5. Dagenham & Redbridge or Salford City
6. Carlisle United
7. Yeovil Town
8. Doncaster Rovers
9. Rotherham United
11. Gillingham or Cheltenham Town
14. Burton Albion
15. Colchester United
16. Northampton Town or Cambridge United
17. St Albans City
18. Shrewsbury Town
19. FC Halifax Town
21. Rochdale or Notts County
22. Kidderminster Harriers
23. Wigan Athletic or Solihull Moors
24. Boreham Wood
26. Ipswich Town or Oldham Athletic
27. AFC Wimbledon
28. Harrogate Town
29. Hartlepool United or Wycombe Wanderers
31. Swindon Town
32. Bolton Wanderers or Stockport County
33. Charlton Athletic
34. Oxford United or Bristol Rovers
35. Tranmere Rovers
36. Leyton Orient
37. Milton Keynes Dons or Stevenage
38. Lincoln City
39. Port Vale
40. Gateshead or Altrincham