Town came into this on a four-game unbeaten run, and looked set for a hard-fought win thanks to a goal early in the second half by the excellent Danny Haynes.
Haynes also hit the bar before limping off injured and then Leeds took control, pegging Town back and forcing a series of corners, and from one ref Phil Crossley saw a handball and penalty-king David Healy drove home the spot-kick.
The match was played at a fast pace throughout, with play switching from end-to-end, although in the first half there were few clear-cut chances.
Gary Kelly curled an early 20-yard free-kick over before the pacy Haynes beat his marker and saw his snapshot from a tight angle tipped over by Neil Sullivan.
Jason De Vos and Richard Naylor got their heads to Jim Magilton (only playing because Darren Currie was held-up in traffic) corners but couldn't find the target before Shane Supple got down swiftly to parry Richard Cresswell's shot on the turn.
Supple saved a Rob Hulse header from a Kelly cross before Sullivan stretched to punch a Matt Richards cross from off the head of the lurking Alan Lee.
Supple then saved a low Liam Miller drive and made his best stop of the half when the ball spun up in the box to Hulse, but the Town 'keeper was out swiftly to block at point-blank range.
Town went ahead on 48 minutes when Supple raced out of his area to head clear, Richards played the ball on and Haynes was suddenly clear and kept cool to slot low past Sullivan.
Leeds' defence couldn't handle Haynes' pace and he broke away past Paul Butler onto another Richards pass, cut inside and thrashed a shot against the bar on 55 minutes.
Lee tested Sullivan with a low 20-yarder before Supple made a magnificent reaction save to block a close-range volley from Hulse after he beat De Vos to a flighted cross from Eddie Lewis.
Haynes had a shot blocked after a neat passing build-up, but aggravated an earlier knock and had to go off midway through the second period, leaving the field to a standing ovation.
That turned the game as Ipswich seemed to try and contain Leeds and the visitors took up the invitation and pegged the hosts back for much of the rest of the game.
Jonathan Douglas had a shot blocked from a Lewis knock-down and then, with three minutes left, came the decisive moment which gifted the visitors the chance to level.
Lewis swung in a right-wing corner, De Vos raised his arm but seemed to miss the ball, it struck Owen Garvan in the chest and he hooked it away, only for Crossley to point to the spot.
Garvan was booked for arguing before sub David Healy kept his cool to send Supple the wrong way, a decision which infuriated Blues boss Joe Royle, who was spoken to by Crossley after hurling a water bottle a little too close to the fourth official.
Town had a handball shout of their own when De Vos met a Currie corner in stoppage time, but it had actually struck a defender's knee, and then Garvan had a shot blocked after a Currie cross dropped to him just inside the box.
In the final seconds, Leeds looked to have a good chance of a breakaway goal with a man over, but Healy had strayed offside before he received Cresswell's pass, and in the end a draw was probably a fair outcome, despite the nature of the Leeds leveller.