The Cobblers - who famously dumped Liverpool out of the previous round - came into Tuesday night's fourth-round tie languishing in 91st place in the Football League ladder but looked set for another shock when Liam Davis put them ahead early on.
But goals from Carlos Edwards and Damien Delaney soon had the Championship side in front and Keane's men turned in a professional second-half display to seal their progress with Tamas Priskin adding a late third.
Keane named a strong side with just three changes from the XI which lost at Nottingham Forest on Saturday while opposing boss Ian Sampson made two changes of his own.
Ipswich striker Priskin had the first sight of goal but took too long to get on the end of Gareth McAuley's knock down before Kevin Thornton tested Ipswich goalkeeper Brian Murphy with a low shot from range.
Priskin then arrowed in a powerful effort from wide on the left but Cobblers number one Chris Dunn was well behind it.
Dunn was then alert to beat Priskin to a long through-ball before the Cobblers forged ahead in the 16th minute.
A lovely passing move saw Billy McKay and Thornton combine to free Davis in space 30 yards from goal.
The left-back was allowed to cut inside onto his favoured left and struck a speculative shot which dipped over Murphy's head and found the roof of the net with the aid of a slight deflection.
The lower league strugglers were settling into the rhythm which they had displayed at Anfield with Thornton to the fore but Keane's men soon responded through Edwards in the 26th minute.
Jason Scotland powered through a flimsy challenge before rolling the ball wide to Edwards. Davis crucially lost his footing which allowed the former Sunderland winger to step into the area and hammer a fine drive past Dunn and into the top corner.
Scotland then fed Priskin to shoot at Dunn as the hosts stepped it up a gear before the keeper parried a stinging Grant Leadbitter shot around the post for a corner.
The 44th-minute corner was to prove costly however as Delaney reacted first to hammer in a loose ball past Dunn at his near post.
Delaney had the first effort of the second period but smashed over the top before Andros Townsend lashed in another powerful effort which Dunn fielded well.
Michael Jacobs then had a rare chance for the visitors when he intercepted Leadbitter's poor pass but the teenager - who had scored at Liverpool - lost his composure to fire wildly over the top.
Dunn was again brave to deny Priskin as Keane's men looked for the killer third goal and despite some late pressure from Sampson's men extended their lead in the 88th minute when Priskin flicked in a header from Leadbitter's curling free-kick.