The Republic of Ireland midfielder - who had netted only two goals since his move from Charlton - was one of nine changes by manager Steve Bruce for the clash against the team he lifted the Milk Cup with back in 1985.
The Mackems were, though, still far too good for City, whose main concern under new boss Paul Lambert will be getting back into the Coca-Cola Championship at the first attempt.
Teemu Tainio set the ball rolling after 26 minutes, and then Reid netted a well-taken double to put the tie beyond Lambert's men before half-time.
Wes Hoolahan reduced the deficit just after the hour, only for Owain Tudur Jones to quickly deflect a corner into his own net.
Norwich finished with only nine men when defender Michael Spillane was sent off for a professional foul on Frazier Campbell, and keeper Ben Alnwick suffered up a cut to his face.