Giovani Dos Santos scored his first Town goal to grab the Blues a point against Burnley at Portman Road. In the first half, after Town had missed two early chances to go in front, Wade Elliott had netted for the visitors.
The Blues made two changes to the side which won 1-0 at Reading on Saturday, Dos Santos starting in the advanced central role in a diamond formation midfield with Alan Quinn dropping out. At the back, Iván Campo returned for Pim Balkestein.
Town started unusually strongly and in the eighth minute Dos Santos was played in on goal by Civelli but the Mexican international chipped the ball into the arms of Burnley keeper Brian Jensen when he should have scored.
Moments later, there was a scare at the other end when a corner struck Jon Stead and fell at the feet of Rhys Williams, whose shot was blocked by Iván Campo.
Town had another golden opportunity to score in the 18th minute. Dos Santos found Civelli in space on the left and the midfielder brought the ball in on goal only for the advancing Jensen to block his effort.
Play immediately moved to the other end, Campo missing the ball as it came through into the area towards Wade Elliott. The former Bournemouth man sold a dummy to Gareth McAuley and Ben Thatcher and lashed a shot past Richard Wright and into the net.
The goal gave the visitors, who had hardly been in the game up until then, a big lift and left the Blues somewhat deflated. On 26 Wright saved from Chris Eagles, then Steven Caldwell headed wide from a corner having lost marker Jon Stead.
On 32 David Wright made a fantastic run into the area from the right. The full-back's shot deflected across goal, but Jon Stead couldn't add the final touch.
Burnley should have added to their lead in the 34th minute when Eagles crossed from the right and Richard Wright saved Elliott's header at point blank. Martin Paterson looped the rebound on to the roof of the net.
At the other end, Stead failed to make contact with Civelli's corner, then Dos Santos's cross flew just behind Lisbie. David Norris's shot through to Jensen in the 40th minute was the half's final goalmouth action.
Town had started the half strongly and should have been in front prior to Burnley's goal, which at the time came against the run of play. Thereafter, the Clarets had the better of the half, although the Blues came back into the game more towards the break.
New signing Dos Santos started the game brightly but drifted out of the match after the goal. This prompted a half-time switch which saw the Mexican go to right midfield and David Norris move to the centre.
Burnley's Paterson struck the second half's first effort, Richard Wright pushing the ball around the post.
Town should have got back on terms in the 49th minute when Jon Stead flicked on a long ball, Kevin Lisbie beat two defenders with a deft touch but then slipped the ball wide of the post with Jensen beaten.
The Blues were pushing for an equaliser and on 54 Norris crossed and McAuley headed over.
Paterson was booked for a pointless foul on Campo on 56, referee Ron Shoebridge having been surprisingly lenient towards one or two earlier Burnley tackles which would usually have resulted in cautions.
The Clarets almost added to their lead in the 61st minute when Robbie Blake's freekick was headed goalwards by Caldwell, Richard Wright doing well to block when a goal seemed certain. Pablo Couñago replaced Kevin Lisbie, then a couple of minutes later Owen Garvan took over from David Norris.
Ben Thatcher shot wide off Pablo Couñago from 25 yards in the 68th minute, before Giovani Dos Santos got Town back on terms. The Mexican received the ball wide on the right and at great speed brought the ball forward into the area past a number of defenders before unleashing an unstoppable shot which beat Jensen to his right.
Alan Quinn replaced Tommy Miller as Town now went looking for the winner. On 76 Garvan curled a freekick to Jensen after Dos Santos had been somewhat cynically felled just outside the right of the area by Christian Kalvenes. Again referee Shoebridge kept his cards in his pocket.
With 10 minutes remaining, Campo lost out to Blake on the Burnley right, but McAuley and then Wright snuffed out the danger.
Wright saved from Chris McCann on 82, then Dos Santos just failed to get anything on Quinn's cross from the right from six yards.
Town keeper Wright again did well when diving at McCann's feet as Burnley broke, but it was the Blues looking most likely to score in the closing stages.
Pablo Couñago forced Jensen into the game's final save with a shot from 20 yards which the Dane pushed away.
In injury time, Luciano Civelli went off on the stretcher tractor with what looked like a serious knee injury having collapsed in pain while chasing down a defender just outside the Burnley area. Town had used all their subs and played the remaining seconds of injury time with 10 men.
Overall, certainly a better display than against Southampton a fortnight ago and Town at times played some good stuff. However, the Blues missed three excellent chances, two in the early stages, and could well have had the game won prior to Burnley's goal.
After that Town showed some nervousness and the Clarets could have gone further in front before Dos Santos's excellent equaliser. The Mexican often found it hard to get into the game, but when he was involved showed quality, pace and an eye for a pass and a goal.
The Blues also had one or two dodgy moments at the back with Richard Wright again in fine form and a draw was probably the right result.
The draw leaves Town five points from the play-offs but requiring a number of teams to severely slip up in the weeks to come and a consistent run of wins if they are to make it into the top six.
Town: R Wright, D Wright, McAuley, Campo, Miller (Quinn 62), Dos Santos, Norris (Garvan 64), Civelli, Lisbie (Couñago 61), Stead. Unused: Supple, Balkestein. Att: 18,745.