The Iron trailed 3-0 at half-time but fought back to force extra time after seven second-half goals left the scores tied at 5-5.
And after winning the penalty shoot-out at Pride Park 7-6, they will now look for another scalp in the form of Chris Hughton's Canaries.
Norwich are one of several Premier League sides who come into the competition at the second-round stage, with those in Europe this season receiving a further bye to round three.
Leyton Orient also earned a top flight away trip via penalty shoot-out drama with their upset of Charlton leading to a tie at Everton.
West Ham host Crewe Alexandra, Swansea entertain Barnsley and QPR welcome Walsall while Wigan Athletic travel to Nottingham Forest and Fulham visit Sheffield Wednesday.
Five-times winners of the competition Aston Villa begin their run at home to Tranmere, while Burton Albion make the short trip to Leicester City in the derby fixture of the draw.
All second-round matches take place in the week commencing August 27.
DRAW IN FULL:
Preston v Crystal Palace
Watford v Bradford
Swansea v Barnsley
Yeovil v West Brom
Coventry v Birmingham
West Ham v Crewe
Doncaster v Hull City
Carlisle v Ipswich
Reading v Peterborough
Sheffield Wednesday v Fulham
Leicester v Burton Albion
Burnley v Plymouth
QPR v Walsall
Stevenage v Southampton
Nottingham Forest v Wigan
Stoke v Swindon
Aston Villa v Tranmere
Crawley v Bolton
Gillingham v Middlesborough
Northampton v Wolves
Everton v Leyton Orient
MK Dons v Blackburn
Leeds v Oxford United
Sunderland v Morecambe
Norwich v Scunthorpe
