Midfielders Richie Ryan and Richard Hinds scored the crucial goals.
It has been a good draw for all our local sides - the Cods will host Tottenham Hotspur, Lincoln will travel to Fulham and Doncaster will play Manchester City.
Second round ties are scheduled to be played on Wednesday September 21.
Holders Chelsea have immediately been installed as favourites to win the Cup, they enter at the third round stage due to their involvement in the Champions League.
Birmingham are rated as tenth favourites by bookies William Hill at 25/1.
Draw in full: Watford v Wolves, Wycombe v Aston Villa, Wigan v Bournemouth, Charlton v Hartlepool, Fulham v Lincoln, Yeovil v Millwall, Doncaster v Man City, Blackburn v Huddersfield, Leicester v Blackpool, Rotherham v Leeds, Norwich v Northampton, Scunthorpe v Birmingham,
Sheffield Wed v West Ham, Burnley v Barnsley, Grimsby v Tottenham, Cardiff v Macclesfield, Mansfield v Southampton, West Brom v Bradford, Gillingham v Portsmouth, Crystal Palace v Coventry, Barnet v Plymouth, Shrewsbury v Sheffield Utd, Sunderland v Cheltenham, Reading v Luton.