Burnley were denied at the death as Alan Lee cancelled out Kyle Lafferty's stunning late strike with a controversial penalty.
Lafferty looked to have grabbed victory for the Clarets with a stunning 85th minute goal.
But in the 90th minute, Town were awarded a penalty for hand ball that former Claret Lee rolled home to rescue a point.
Burnley spent the week digesting the news that leading scorer Andy Gray will be sidelined until February with three broken metatarsals.
However, that opened the door for hungry teenager Lafferty, who stepped into Gray's shoes at Portman Road for his first start in a month.
The only other change from the midweek victory over Leeds saw a start for Chris McCann, who was preferred to Micah Hyde in central midfield.
But it was Lee who almost made a name for himself inside the opening two minutes with a header just side of Danny Coyne's right hand post.
Lafferty, an integral part of the new breed at Turf Moor, then had a great early chance with Burnley's first genuine threat in the 12th minute, curling the ball into Lewis Price's grateful arms when trying to find the far corner.
Ex-Town favourite John McGreal headed straight at Price from a deep Steve Jones corner as Burnley continued their lively start.
And Burnley were left wondering how they failed to take the lead in the 25th minute following another great move down the left.
This time Jones - in acres of space - crossed hard and low for Lafferty, whose goalbound touch struck defender Jason De Vos and then Price before being hacked to safety at the far post from Wade Elliott's follow up attempt.
The visitors were totally in the ascendancy, but Town handed them a timely warning of their own attacking prowess on the half hour mark.
Livewire striker Billy Clarke left Michael Duff in his wake and unleashed a rising drive from 25 yards that Danny Coyne turned for a corner at full stretch.
Half time arrived with Steve Cotterill undoubtedly happier than his Town counterpart Jim Magilton.
But the Town manager was scratching his head in disbelief three minutes after the restart when Sylvain Legwinski somehow failed to give the hosts the lead.
The Frenchman rose unchallenged inside the six yard box to connect with Gavin Williams' pinpoint cross, but somehow Danny Coyne plucked his point-blank header out of the air on the goal line.
And Lee then missed a similar golden opportunity, blazing hopelessly wide when bearing in on goal with just Coyne to beat.
The Clarets were coming under increasing pressure as the Tractor Boys built up a head of steam.
But Gifton Noel-Williams headed just over the crossbar and McGreal's far post header was hacked off the line as Burnley looked to seal victory themselves in the final quarter of the game.
Micah Hyde's 73rd minute introduction for Elliott allowed Lafferty to drop to right midfield and Jones replace him up top.
Jones could have won it for the Clarets as he used his pace to race in behind De Vos, only to fire at Price as he advanced from his line.
Lafferty then thought he had won it when he picked up the ball on the right, cut inside and unleashed a stunning low drive that flew past Price and into the bottom corner.
But the real drama was yet to come and referee Keith Hill pulled up Noel-Williams for hand ball in a melee and Lee did the rest.
BURNLEY: Coyne, Thomas, Duff, McGreal, Harley, Elliott (Hyde 73), J O'Connor, McCann, Jones (Sinclair 88), Noel-Williams, Lafferty.
Subs not used: Jensen, Foster, Mahon
Booked: Lafferty 45, McGreal 68, Thomas 69, Noel-Williams 90
IPSWICH: Price, Richards, De Vos, Bruce, Naylor, Garvan, Legwinski, Williams (Haynes 80), Lee, Clarke (Peters 68) , Roberts.
Subs not used: Macken, Castro, Supple
Ref: K Hill
