Matt Richards's last minute goal gained Town a draw from a largely turgid game at Portman Road. The visitors, who spent most of the 90 minutes frustrating the Blues, went ahead in the 19th minute when Robbie Blake scored his seventh of the season.
Central defender Jason De Vos recovered from his toe injury sufficiently to take his place at the heart of the Town defence. Lewis Price continued in goal, while Ian Westlake returned to the midfield as the Blues switched to 4-4-2, Darren Bent missing out due to his hamstring problem.
Skipper Jim Magilton looped a header goalwards early on but Danny Coyne saved with little trouble. At the other end there was a scare for Lewis Price when former Blue, John McGreal - given a fine welcome by his old fans - nipped in ahead of him as he sought to claim a corner. Fortunately for the Welsh U21 keeper the ball fell to a Town defender.
Magilton had another go at goal with his head in the ninth minute, nodding Dean Bowditch's deep cross to Coyne's right but within the former Grimsby man's reach.
Burnley had made their in the main defensive intentions clear from the off but, as so often, they went ahead with their first attempt on goal.
Richard Naylor got caught in possession by Micah Hyde in the 19th minute, the former Watford man playing the ball across the penalty area to Robbie Blake who gave Price no chance.
A Blake cross caused a fair bit of panic in the Town box on 26 but no Burnley player managed to get in a shot and the danger was cleared.
A minute later the Blues should have had a penalty. Bowditch played the ball inside from wide on the left to Westlake, whose cross was clearly handled out of play by Frank Sinclair.
It appeared impossible for both referee Brian Curson - already annoying fans for failing to pick up on remarkably early Burnley timewasting - and his assistant to miss it but miss it they did. From the corner awarded instead of the penalty Kuqi headed just wide.
On the half hour, Dean Bowditch almost got on to a Naylor through ball as Town massively dominated possession without creating too many clear-cut chances.
Hyde picked up a yellow card for a late tackle on Tommy Miller, before Drissa Diallo headed a Bowditch cross over the bar. Not long after, Bowditch himself shot over from the left side of the penalty area. Late on, a rare Burnley attack saw an Ian Moore shot saved by Lewis Price.
By no means a vintage half, however, Town didn't really deserve the boos which came their way from some in the crowd at the whistle. Burnley's massed defence was proving difficult to break down and the Blues had had little help from the referee who had turned down a cast iron penalty.
Two minutes after the break Town hit the woodwork through Kevin Horlock. The former Manchester City man curled a freekick from 25 yards over the wall but off the top of the bar and out of play. On 49 Joe Royle replaced Dean Bowditch with Pablo Couñago, giving the Spaniard a chance to answer his manager's criticisms.
Burnley came out in the second half with if anything a more defensive attitude than in the first, their 4-5-1 formation looking more like a 4-6-0, with the midfield sitting particularly deep. But on a rare foray forward in the 53rd minute, Blake forced a save from Price.
Just after the hour, a superb Jim Magilton pass put Shefki Kuqi in the clear on the right of the penalty area but his shot flashed across the face of goal.
Blake almost put the visitors further ahead on 67 when he cut in from the right before hitting a low shot which Lewis Price did excellently to get down to his left and hold on to. A minute later Price made another save, this time from Graham Branch but the Town keeper was involved little in the remaining 22 minutes.
Couñago headed a Magilton corner wide on 69 as the Blues continued to look for an equaliser and on 74 they should have been back on terms. Kuqi found Diallo wide on the right, the Guinean crossed deep to Westlake who took an age about shooting.
When he did so the ball was on its way well wide until it struck Kuqi and went back out to the left flank. The Finn headed Westlake's subsequent cross wide.
In the 78th minute Couñago was handed a fantastic opportunity to score when Magilton played him through one-on-one with the keeper on the edge of the six-yard box from a quickly taken freekick. Coyne came off his line quickly and blocked as the Spaniard delayed his strike.
With four minutes of normal time remaining, Coyne pulled off a fine save low to his right as Westlake helped on a Richards cross shot from the left.
As the end of the 90 minutes drew close, a goal finally came. Richards crossed deep from left and Kuqi forced another fine save from Coyne with his header. Defender Camara went to ground - the latest in a succession of timewasting tactics employed since they went ahead - but Town kept playing.
The ball was eventually played out to Kuqi on the right, the striker cutting in and laying a ball across the box, Westlake missing it but Richards lashing it in off the far post from a tight angle on the left.
Once the goal had gone in, Town seemed to get the bit between their teeth and went looking for a winner in the five minutes of injury time, a conservative estimate of the amount of time wasted by Burnley and particularly keeper Coyne during the scheduled 90.
Around a minute into added on time, Couñago laid the ball back to Miller on the right of the area and midfielder crashed a shot off bar and then post, Coyne saving Couñago's rebound. It seemed amazing that the ball hadn't gone in from Miller's well-struck effort.
Late on Lee Roche picked up a yellow card for a cynical foul on Ian Westlake just outside the area as the midfielder brought the ball forward inside the Burnley area.
Miller and Couñago's strikes were to prove Town's last of a game which only really got going when Richards scored his last minute equaliser.
The Clarets' negative attitude prompted chants of 'boring, boring Burnley' before the end and ruined the game as a spectacle.
Town had more trouble breaking down McGreal et al than they have other sides coming to Portman Road with a similar approach of late but deserved at least a point from a game which they dominated throughout.
The Blues won't be the only side to be frustrated by Burnley this season and they will feel unfortunate not to have got more out of the game, the referee missing an obvious penalty and the woodwork denying them on a number of occasions.
Town: Price, Diallo, Richards, De Vos, Naylor, Magilton, Miller, Horlock, Westlake, Bowditch (Couñago 49), Kuqi.