Burnley made it six straight wins to stay at the top of the Championship with a first victory at Portman Road since 1970.
Town had the better of the chances in the first-half and Cole Skuse twice went close just before the break but the only goal of the game came 11 minutes from time when Scott Arfield sent a header skimming into the Town net.
Mick McCarthy stayed with the same side that drew at Sheffield Wednesday before the international break, Jack Marriott taking a place on the bench in the only change to the 18.
Town started brightly against the in-form Clarets, Ryan Tunnicliffe seeing a shot deflected, then Jason Shackell blocking David McGoldrick’s effort at the near post.
Burnley took a while to get going and had only Arfield’s tame shot to show for their first 20 minutes work as Blues forced the visitors back.
McGoldrick spun inside the Clarets’ box but his shot lacked power but Sean Dyche’s side began to get a foothold in the game and from the best move of the first-half, David Jones sent Kieran Trippier clear on the right and his cross skimmed across the goal as Sam Vokes threatened an opener.
Michael Kightly almost capitalised on a mis-placed pass by Christophe Berra but Tommy Smith was in the right place to clear, then at the other end Paul Anderson climbed well to meet a cross but couldn’t keep his header down.
Town were forced into a change seven minutes before the break when Dean Gerken limped off, Scott Loach on for his first appearance since August.
Town finished the half with a flurry, Skuse’s shot beaten out by the Burnley defence on the line after Tom Heaton had failed to clear the danger, then the midfielder had the crowd off their feet when he sent a 20 yarder past the Clarets’ ‘keeper but inches wide of the post.
Town were inches away again as the second-half got underway. An in-swinging free-kick from Aaron Cresswell was met by Berra but Heaton stood firm as the ball landed in his hands.
Luke Chambers timed his challenge to perfection to rob Vokes in the box as Burnley responded, then an inventive backheel by McGoldrick released Cresswell for a right foot strike that brought handball claims by the Town players as both sides searched for the breakthrough.
Anderson fizzed a low shot just wide for Blues, while Loach got down well to smother Kightly’s right foot drive.
McGoldrick sent a header a foot over before the Clarets went in front 11 minutes from time, Arfield getting on the end of Trippier’s cross and flashing his header into the far corner.
Frank Nouble replaced Daryl Murphy for the last five minutes, Jay Tabb on for Anderson in a double change as Blues chased an equaliser, Tabb so close to getting in from McGoldrick’s subtle pass.
Danny Ings fired wide on a break in the last opening of the game that looked destined to stay goalless until Arfield's excellent finish maintained the Clarets' terrific run.