It set the tone for a committed performance by the Cobblers, who scored a first victory over Norwich since 1963.
Cobblers boss Martin Wilkinson was a delighted man, but admitted: "I would rather have had the three points against Torquay on Saturday."
His opposite number Nigel Worthington was left to reflect on a night when the Canaries created their share of chances, particularly in a high-powered 20-minute spell at the start of the second half. But they could not find a way past Glyn Thompson.
Worthington said: "We were very committed and worked hard, but we went to sleep on the set piece from which Northampton scored."
He added: "I brought our two young lads Ryan Jarvis and Ian Henderson into the attack because David Nielson and Paul McVeigh worked their socks off in the heat at Bradford on Saturday."
It is the third season running that Norwich had ducked out at the first hurdle after previous defeats by Cheltenham and Brentford, while Northampton were enjoying their highest profile cup success since beating West Ham in the second round in this competition in 1998.
Norwich's best chances to get on terms came from a Mark Rivers header in the 12th minute which should have been at least on target, while Henderson skipped clear of the home defence midway through the second half only to chip wide when a goal appeared a certainty.
The impressive Low could have added to his tally, spoiling some great approach work by firing weakly just after the break.
Paul Trollope was just inches wide with a first-half drive and Low almost added the icing on the cake nine minutes from time when his goalbound shot was cleared off the line.
Northampton: Thompson, Chambers, Willmott, Reid, Clark, Low, Trollope, Reeves, Burgess, Richards, Martin Smith. Subs: Sampson, Dudfield, Hargreaves, Harper, Asamoah.
Norwich: Green, Edworthy, Mackay, Fleming, Drury, Rivers, Holt, Francis, Easton, Henderson, Jarvis. Subs: Briggs, Nielsen, Mulryne, Crichton, McVeigh.
Referee: Ray Olivier (W Midlands).
Attendance: 5,476