Town remain without a win in the competition since 2019 after goals from Emile Acquah, Tom White and Ben Whitfield secured the Bluebirds' passage through to the second round.
Jon Brady’s side were punished for slack defending by Acquah’s early header but they grew into the game and were back on level terms by the break thanks to Mitch Pinnock’s somewhat fortuitous equaliser.
It looked as if Cobblers had the momentum and would take control of the game from there, but instead White’s fortunate deflected strike and a late defensive mix-up saw them beaten in the first round for the fourth year in a row.
Brady was without first-choice goalkeeper Lee Burge due to injury so Max Thompson started between the sticks, and there were also recalls for Jordan Willis and Will Hondermarck, who replaced Manny Monthé and Tyreece Simpson. Louis Appéré and Jack Sowerby returned to the bench.
Cobblers were slow to get going and paid the price when Barrow took a ninth-minute lead.
It was as simple as you like for the League Two side as Elliot Newby delivered a corner into the box and Acquah barely had to jump to head into the top corner.
There was an edginess around Sixfields, both on the pitch and in the stands, as Town dominated possession but struggled to inject any purpose into their play, although Hondermarck curled narrowly wide and Sam Hoskins had a shot well blocked.
It would have been a stretch to say that a goal was coming but Cobblers were level in unusual circumstances just before the half-hour mark.
Niall Canavan’s attempted clearance from the right channel was charged down by Hoskins and the ball looped up in the air and fell perfectly for Pinnock who finished well having found himself all alone in the penalty box.
Town gained some confidence from the goal and Marc Leonard followed it by dragging a shot wide, but Barrow were almost back in front through Dom Telford’s superb long-range strike which whistled fractionally wide of Thompson’s goal.
The home side were in the ascendency though and they carved out a good opportunity to take a lead into half-time after Pinnock slipped in Hoskins whose cross-shot was poked wide by a sliding Hondermarck.
Another presentable chance went begging at the start of the second half as Hoskins steered wide after being released by Akin Odimayo, and Barrow took advantage of that let-off by retaking the lead when White’s speculative effort took a wicked deflection and gave Thompson no chance.
Cobblers once again had to come from behind and they were finding it tough against the organised and well-drilled visitors, with Hoskins heading a rare chance onto the roof of the net.
Town’s fate was sealed with a terrible mix-up at the back with 18 minutes to play when Ali Koiki and Thompson got in each other’s way and Whitfield nipped between the two and poked the ball into an unguarded net.
Thompson made a decent save from Jamie Proctor to prevent further damage late on but Town’s race had been run and another first round exit was duly confirmed at full-time.
Cobblers: Thompson, Odimayo (McGowan 56), Sherring, Willis (Sowerby 67), Brough, Koiki (Monthé 77), McWilliams (Simpson 77), Leonard, Hondermarck (Appéré 67), Pinnock, Hoskins ©. Subs not used: Dadge, Lintott, Haynes, Dobson
Barrow: Farman, Mazeed, Canavan ©, Ogungbo (Gotts 45), Ray, Spence, Newby, White, Chester (Foley 74), Stephenson (Whitfield 45), Acquah (Proctor 61), Telford (Garner 61). Subs not used: Duffus, Bray, Etaluku
Referee: Paul Howard
Barrow fans: 168