Jewell opted to rest the majority of the side that defeated Bristol City 3-0 on Saturday, with Aaron Cresswell and Jay-Emmanuel Thomas the only players to keep their place.
Emmanuel-Thomas gave the Championship side an early lead, but goals either side of half-time from Ben Tozer and Paul Turnbull ensured Northampton avenged their 3-1 defeat at Portman Road in the fourth round of last season's competition.
After Bas Savage, one of two changes to the Northampton team that drew 0-0 with Accrington at the weekend, had missed an early header, Emmanuel-Thomas opened the scoring in the 11th minute.
The former Arsenal forward picked the ball up from Cresswell on the left and beat Sam Walker with a superb shot into the far corner.
Emmanuel-Thomas came close to a second soon after, but Northampton retained an attacking threat of their own and saw Jake Robinson and Arron Davies spurn opportunities.
Ipswich's Jason Scotland then forced Walker into a fine save, yet the Cobblers pulled level six minutes before the break. Tozer's first effort was saved by Arran Lee-Barrett, but the midfielder reacted first to slot home the rebound.
Byron Webster's block prevented Scotland from restoring Ipswich's lead and Northampton duly moved in front after the interval, Turnbull converting from close range after Davies had flicked on a cross.
Michael Jacobs curled a shot over from 12 yards and Savage forced Lee-Barrett into action as the visitors threatened to extend their advantage.
By the closing stages, however, they were hanging on and Emmanuel-Thomas headed wide from close range before testing Walker with a free-kick, either side of substitute Lee Martin going close with an ambitious 30-yarder.