The hosts began the tie as the stronger of the two teams, as Manchester United loanee Ethan Wheatley hit the post after just 10 minutes.
The 19-year-old forward, who has played three games for the Red Devils in the Premier League, entered the Chairboys' box and tried to place the ball just beyond Mikki Van Sas, but struck the woodwork.
Wanderers rarely threatened in a poor first half, with their best chance falling to Caolan Boyd-Munce, as his bending left-footed inswinging corner crashed the crossbar.
James Tilley also tried his luck, but his attempt was blocked, in what was a flat opening 45 for the Chairboys.
The Cobblers took control as they took the lead on 26 minutes.
A swift counterattack from their own box eventually found Wheatley, whose low ball into the found Kyle Edwards, who struck it first time beyond Mikki Van Sas.
It was the forward’s first goal for Northampton since his summer move from Stevenage.
Kevin Nolan’s team continued to show their dominance as Elliott List headed wide from a Wheatley cross before they got their second five minutes before the break.
Tyrese Fornah, who had also never scored for the Cobblers, struck it on the half-volley on the edge of the box.
Van Sas managed to get a huge hand on it, but not enough to keep it out, as Northampton doubled their lead.
The second half saw Wanderers go close as Donnell McNeilly forced Lee Burge into a good save, while Armando Junior Quitirna saw his first-time shot go wide.
The result means Wycombe have been eliminated from the competition at the round of 32 stage for a second consecutive season.
For Northampton, it ends a torrid run of 10 games without a win versus the Chairboys.
Their last victory against Wycombe came in February 2016.
Since then, Wanderers have won eight and drawn two of the next 10 meetings ahead of tonight’s clash.
Up next for the Adams Park side is an away trip to Exeter City in the FA Cup on December 5.