Colin Calderwood continues to transform fortunes at Sixfields, and this eye catching success against the Division Two leaders means the Cobblers have now been beaten only once in 7 games under his charge.
Plymouth were strongly fancied to make the second round, but they wasted a series of decent chances in the first half and paid the penalty when substitute Derek Asamoah scored a dramatic winner seven minutes from time.
Argyle went in front in the 32nd minute when leading scorer David Friio bagged his ninth of the season from the edge of the box after the home defence failed to deal with a corner.
But Northampton were back on terms five minutes later when on-loan striker Richard Walker applied the finishing touches to a cross from Des Lyttle with Argyle's defenders still complaining about a quickly taken corner.
Chris Hargreaves enjoyed a special moment on the hour when the Cobblers midfielder netted from close range against the club he left three years ago. But the home joy was short lived as Ian Stonebridge struck a 63rd minute leveller.
Stonebridge scored when the sides met here in a 2-2 draw at the end of last season and the striker was in the right place when a Paul Wotton free kick was deflected into his path, leaving him with a clear-cut chance. Both sides had chances to clinch the tie before Northampton did that.
Walker could have had his second in the 79th minute but curled a right-foot shot wide while Argyle substitute Lee Hodges blasted a left footer which screamed inches wide of Lee Harper's left hand post.
But with time running out, Asamoah skipped clear of a challenge by David Worrell and kept his cool to beat Luke McCormick from just inside the box.
Delighted Northampton boss Calderwood said; "This was a great result for us. I certainly didn't fancy the replay back at Plymouth and I am delighted for the lads."