Freddie Sears celebrated signing a new four year contract by setting Town on the way to a third successive home win.
The striker - who put pen to paper three hours before kick-off on a deal that keeps him at Portman Road until 2019, with a year option - opened the scoring with a sublime finish midway through the second-half.
David McGoldrick then put Blues firmly in the driving seat with a header from a corner five minutes later as Town maintained the unbeaten start to the season and moved to the top of the Championship table.
Mick McCarthy stayed with the same side that beat Sheffield Wednesday on Saturday, Sears immediately in the action with a cross from the right held by Tom Heaton.
Burnley went close to opening the scoring when Michael Kightly rattled the inside of the post and bounced into the grateful arms of Bart Bialkowski.
Neat link-up from Luke Chambers and Ainsley Maitland-Niles on the right saw the skipper have an effort deflected for a corner, then from the flag kick, Jonathan Douglas couldn’t get his shot in.
Cole Skuse sent a 30 yarder over after Jonas Knudsen had set him up, then Maitland-Niles dragged his shot wide of the target.
Daryl Murphy couldn’t keep his shot down after Knudsen had found him in an even opening to the game.
George Boyd volleyed over from the edge of the box but Town were forced to make an early change, Ryan Fraser limping off with a knee injury to be replaced by McGoldrick.
The striker saw a left footed effort cleared by Michael Duff inside the Clarets’ box as he looked to make an immediate impression.
Sears exploded a shot at Heaton after Tendayi Darikwa gave the ball away, Bialkowski in the right place at the other end to force Jelle Vossen’s shot away.
David Jones’ free-kick was inches over just before the break as an evenly contested first-half came to an end goalless.
Blues made a second change at the break, with Brett Pitman replacing Murphy, Tommy Smith mistiming his header from a Matiland-Niles corner as the half got underway, McGoldrick heading over soon after following another delivery from the Arsenal loanee.
Maitland-Niles headed back across goal but Michael Keane cleared as McGoldrick looked to get in and on 65 minutes, Blues got the breakthrough, with Pitman crossing from the right and Sears guiding the ball expertly into the far corner.
Town doubled the advantage five minutes later, Maitland-Niles swung in a corner and McGoldrick got his head on it to find the bottom corner.
Bialkowski held firm from Kightly as Burnley looked to respond but Town held the recently relegated from the Premier League Clarets at arms length.
It was Blues who looked the more likely to trouble the scorers, Douglas ripping a shot wide of the far post, then Sears crowded out inside the box. Keane having Burnley’s final chance with a header saved by Bialkowski from close range.
Giles Coke replaced Maitland-Niles - who was given a standing ovation by the home faithful - for the closing stages as Blues tightened the grip on the game and points that never looked like evading Town after the second goal.