A late own goal by Chris Makin had denied City a win at Coventry on Saturday and they were again foiled against Ipswich when this time Heath put through his own net with just 60 seconds of normal time remaining.
It was a tragedy for the young defender who had looked to have given his side the win with a superbly struck goal on the hour mark to put his side at 2-1 in front.
And all this after the game had got of to the most dramatic off starts with Town racing into the lead inside the first minute.
The crowd hardly had time to settle when Darren Bent raced to a Kevin Horlock throughball and shot straight at Kevin Pressman who had raced of his line to confront the Ipswich striker.
Leicester had thought the danger had passed but Ian Westlake was first to the loose ball and with the keeper stranded lobbed it from 18 yards over a posse of retreating defenders into an unguarded net.
Such an early setback might easily have deflated City, but instead they started to match the visitors fluid midfield and slowly began to pin back Ipswich in their own half.
The Foxes had a clear chance on 25 minutes when Gareth Williams played in David Connolly whose twelve-yard shot was beaten away by Lewis Price.
Connolly had made no mistake in the 33rd minute when he raced onto a James Scowcroft flick on and fired a 10-yard shot across Price into the far corner of the net.
Price denied Leicester a second on 39 minutes when he leapt across the goal to claw away Danny Tiatto's 20-yard drive.
In the dying moments of the first-half Price produced fantastic saves twice to deny Connolly and Westlake and then came to Town's rescue clearing a brilliant header off the line.
City continued to press with a same verve after the break and their enterprise was awarded on the hour mark when Makin's right-wing cross was nodded down by Scowcroft to Heath who scored with a crisp drive from 18 yards.
Pressman then came to Leicester's rescue to deny first Shefki Kuqi and then substitute Pablo Counago.
Town were convinced they had scored four minutes from the end but the effort was disallowed after the referee had ruled an Ipswich player kicked the ball out of Pressman's hands.
But in the 89th minute Ipswich were level courtesy of a tragic error by Heath who headed into his own goal after his fellow defenders had failed to clear a Tommy Miller corner.