Town boss Joe Royle was unhappy on Saturday with the chances his side missed, despite winning 1-0 at Bradford City, and got what he wanted when he asked for cooler heads in front of goal.
The game was over as a contest by half time, at which point Town led 5-0, all the goals coming in a 20-minute period.
Pablo Counago got the first on 20 minutes, collecting an Alan Mahon pass, holding off Dean West and sliding the ball beyond Brian Jensen.
The Spaniard scored again two minutes later, Mahon flicking the ball on for Counago to turn inside Lee Roche and curl the ball into the corner of the net.
Jermaine Wright then got the third on 28 minutes, volleying home a Fabian Wilnis cross beyond the far post, again giving poor Jensen no chance.
Incredibly, Town made it 4-0 on the half hour, Chris Bart-Williams and Wright exchanging passes before the former fired past Jensen from 20 yards.
Paul Weller blazed over from a couple of yards for Burnley before Town scored again after 40 minutes, Shefki Kuqi's shot from Mahon's corner going in off Richard Chaplow for an own goal.
Burnley got a consolation goal four minutes after the break when Town failed to clear a loose ball and Chaplow pounced to cross for Delroy Facey to slot home.
Both sides then hit the woodwork, Town through a curling Jim Magilton free-kick from 20 yards, while Mo Camara also hit the bar with a venomous angled drive.
Ipswich added a sixth goal to secure their sixth win in seven games in stoppage time when substitute Ian Westlake crossed for Kuqi, who controlled the ball and lashed home a left-footed shot.