Two goals in the last five minutes saw honours even at Portman Road with Alan Lee's 90th minute penalty giving Blues a point after Kyle Lafferty looked to have won it for the visitors.
Lafferty cut in on the Burnley right and curled a left foot strike past Lewis Price with only five minutes left on the clock.
Town levelled on 90 minutes, Gifton Noel-Williams judged to have handled Gary Roberts' corner and Lee rattled in his ninth goal of the season, sending Danny Coyne the wrong way from the penalty spot.
Owen Garvan was handed his first home start of the season after recovering from illness, Gavin Williams also in the line-up with Matt Richards taking up the left-back role.
Lee, up against his former club, sent a header wide inside the first 60 seconds, while at the other end Noel-Williams headed back across goal from Steve Jones' cross, Richard Naylor clearing the danger.
Jones and Lafferty worked an opening on 10 minutes, with Lafferty shot lacking pace, with Price making a comfortable save.
Former John McGreal tested Price with a header from a corner, then the lively Jones had a shot deflected wide as Burnley enjoyed the better of the opening exchanges.
Jones spun and shot over as Town retreated, with Billy Clarke repeating the same feat at the other end, his shot belted clear by the covering Wayne Thomas.
Price saved Town on 25 minutes when he clawed away Lafferty's close range flick after Jones had escaped down the Burnley left.
Garvan had a goalbound shot cleared by Thomas as Town stepped up a gear for the closing stages of the half. A flowing move between Garvan and Clarke the best bit of football in the half, with Coyne springing to his right to beat out Clarke 25 yard strike.
A surging run down the right saw Lee escape Michael Duff, his cross falling to Garvan at the far post whose header set up Clarke, Coyne making a low save to his left.
Lafferty picked up the first booking of the match for a foul on Williams, then from the resultant free-kick Naylor went down in the box but referee Keith Hill waved away the penalty appeals.
Town started the second-half on top and Sylvain Legwinski had a gilt edged chance to put Blues ahead two minutes after the restart but his header from Williams' cross went straight at Coyne.
Town carved open the Clarets' defence three minutes later and Lee raced into the box but sliced his shot well wide. The impressive Williams, making his first start 10 weeks following a hernia operation, blasted over.
Jim Magilton's side camped around the box and Garvan forced a corner with a left foot cross, Jason De Vos just failing to get on the end of Gary Roberts' flag kick.
Burnley had their first real opening of the second-half on the hour mark, McGreal heading goalwards from a corner and Noel-Williams beating Price to the ball but his flick header went over the bar.
At the other end, Legwinski also headed over the bar from Williams' cross before Town made a first change, Jaime Peters coming on for Clarke.
Williams was pushed into the 'hole' behind Lee and immediately the Welsh international brought a foul of McGreal, the Clarets' defender cautioned. Thomas quickly followed for a lunge on Roberts.
Micah Hyde replaced Wade Elliott for the last 20 minutes and seconds later Roberts cleared McGreal's header off the line, then the backtracking Price dealt comfortably with Jones' strike as the former Crewe got behind Richards.
Alex Bruce breached the Burnley defence down the Town right with a surging run but his cross was cleared by Duff as Blues searched for that elusive way to goal.
Derby hero Danny Haynes replaced the tiring Williams with 10 minutes left on the clock, with fellow substitute Peters immediately going close with a header over the bar at the near post.
Peters then weaved his way into the box down the Town but his shot lacked direction, sailing well over Coyne's goal.
When the goal finally came it was Burnley who provided it, Lafferty cutting in from the right and curling a left footed strike past Price and into the net.
Legwinski mickicked 18 yards out then Roberts' cross caused mayhem in the Burnley box, the ball cannoning away for a corner. Roberts swung it in, Noel-Williams' hand went up and referee Hill immediately pointed the spot. The offender booked, Lee doing the rest from the spot.
Town: Price, Bruce, De Vos, Naylor, Richards, Williams (Haynes 79), Legwinski,Garvan, Roberts, Lee, Clarke (Peters 67). Subs not used: Supple, Sito, Macken.


















