The goals dried up for Championship leaders Burnley, who must try again at Turf Moor to dispose of Ipswich and reach the FA Cup fifth round.
The League One hosts - who are also top scorers in their division, made a strong start and could have been ahead in the second minute had George Hirst, played in by Kayden Jackson, hit the target.
Marcus Harness went even close straight after with a chip that bounced off the top of the Burnley bar.
Kompany's much-changed side - only four started their last Championship success as well as this one - looked shaky at the back, with centre-back Jordan Beyer shown a yellow card in the opening exchanges.
Jay Rodriguez went close with a rising drive before Clarets keeper Bailey Peacock-Farrell had to tip over an effort from Jackson from a tight angle.
Beyer was lucky to stay on the pitch after bodychecking Jackson as the first half ended goalless.
Darko Churlinov saw a decent Burnley chance deflected over early in the second half before Nathan Tella forced Town goalkeeper Vaclav Hladky into a smart stop.
The Czech was needed again seconds later to bat away an effort from Rodriguez, who fancied his chances of beating him from outside the box.
Ipswich were up against it but defender Luke Woolfenden was on target with a flick after Burnley struggled to clear a corner.
Both sides made a triple substitution around the hour mark, with Burnley then handing a debut to new signing Lyle Foster, the South Africa forward, soon after.
It was fellow sub Anass Zaroury who almost broke the deadlock but the man who bagged a brace in the 4-2 win at Bournemouth in the third round saw his shot deflected just wide.
Town sub Conor Chaplin almost caught Peacock-Farrell out with another cross in stoppage-time but it remained goal-less.