Mackail-Smith clinched the League One side’s passage to the second round by pouncing on a loose ball in the 90th minute.
Last season’s cup heroes Havant & Waterlooville failed to cause an upset at Westleigh Park, where they lost 3-1 to League Two side Brentford.
The Bees opened the scoring in the 41st minute when Marvin Williams tucked home from close range.
Charlie MacDonald added a second after 65 minutes before Ian Simpemba put the hosts back in it with a clinical header seven minutes later. Three minutes from time Elder sealed the win.
Kaid Mohamed’s winner 15 minutes from time gave Forest Green a 1-0 win at Blue Square South side Team Bath, earning a meeting with Barnet or Rochdale.
In Saturday’s ties, Histon caused the shock of the round by beating League One Swindon 1-0, thanks to Daniel Wright’s goal.
Gary Madine saved managerless Carlisle United’s blushes as they drew 1-1 with Blue Square Premier side Grays Athletic, while Jean Francois Christophe’s last-gasp equaliser denied AFC Telford a win over League One Southend.
Blue Square Premier side Droylsden earned a replay with Darlington after playing out a 0-0 draw with the League Two leaders.
FA CUP SECOND ROUND DRAW: Chesterfield v Darlington/Droylsden, Peterborough v Accrington Stanley/Tranmere, Eastwood v AFC Wimbledon/Wycombe, Notts County v Kettering/Lincoln, Leicester v Hereford/Dagenham & Redbridge, Eastbourne/Barrow v Brentford, Bradford v Leyton Orient, AFC Telford/Southend v Luton or Altrincham, Forest Green v Barnet/Rochdale, Histon v Leeds/Northampton, Scunthorpe v Alfreton, Torquay v Oxford/Dorchester, Leiston/Fleetwood v Brighton&/Hartlepool United, Morecambe v Cheltenham/Oldham, Gillingham v Yeovil/Stockport, Millwall v Aldershot/Rotherham, Carlisle/Grays Athletic v Crewe, Bournemouth v Blyth Spartans, Kidderminster v Curzon, Ashton Port Vale v Macclesfield.
Ties played weekend of November 29/30.