A debut goal from French midfielder Bakary Sako earned Wolves a Capital One Cup third-round trip to Chelsea.
The 24-year-old, who joined the club from St Etienne on Wednesday, fired in from 20 yards in stoppage time.
Central defender Danny Batth had scrambled in a 16th-minute goal for the visitors, but boyhood Wolves fan Clive Platt equalised.
Frank Nouble restored Wolves' lead in first-half injury time with another scruffy goal, before Sako struck.
Wolves have been inconsistent in the Championship this season, collecting four points from three games, but were largely in control against their League Two opponents.
After a lively start by the home side, Batth bundled in his first goal for Wolves from Razak Boukari's corner.
Northampton had knocked out last season's finalists Cardiff in the first round, but rarely threatened the Wolves goal until they equalised five minutes before half-time.
Veteran striker Platt, 34, scored it by climbing above Batth to head in Chris Hackett's right-wing cross.
Wolves regained the lead in first-half stoppage time when Anthony Forde headed back a Boukari cross and Nouble saw the ball bounce up off his chest and creep over the line for his first Wolves goal.
Boukari, who had an impressive debut on the right wing after joining from Rennes on Monday, saw a shot blocked by Kelvin Langmead early in the second half after keeper Dean Snedker spilled a cross.
The 17-year-old keeper, making only his second senior appearance, then dived at the feet of Wolves midfielder David Davis, who had been put through by Boukari.
Sako replaced the Togo international midway through the second half, and thumped in a third goal late on.
VIEW FROM THE DRESSING ROOM
Northampton Town manager Aidy Boothroyd told BBC Northampton:
"All I hoped was that the players would give their all and leave nothing on the pitch.
"The manner we conceded the goals was poor but we've got a young boy in goal and he'll get better and better.
"They were sloppy, flukey goals. We had the better chances but that's the quality you're playing against.
"We take it on the chin, say good luck to Wolves in the next round and we concentrate on our league form which is very important for us."