Despite being below their best, Town looked set for a sixth win in seven games when Owen Garvan's low drive whistled past former Ipswich keeper Andy Marshall after just six minutes.
Millwall turned up the pressure in the second half and got their rewards with Livermore's late header from a corner which the home defence couldn't clear.
The game began in lively fashion as both sides went close in the opening two minutes as first Shane Supple dived to save a Paul Robinson header from Zak Whitbread's cross and then Darren Currie put Ian Westlake in and his low left-foot drive flashed across the face of goal.
Currie curled a 20-yarder on to the roof of the net before Garvan beat Livermore to a weak Whitbread header from a Westlake cross and fired a low 20-yard into the net.
Scott Barron did well to block a fierce Tony Craig shot before Currie's ball over the top sent Westlake chasing through, but Marshall raced out to beat him to the ball.
The home crowd were getting frustrated at their side's inability to capitalise on the early breakthrough and Alan Dunne then headed wide from a Craig cross as Millwall kept up the pressure.
Matt Richards drew a low save out of Marshall with a 20-yarder and the half ended with Marvin Elliott firing a 30-yard effort well wide.
Barron did well to block a Dunne shot soon after the break after Craig's cross found its way through a crowded penalty area before Town had two great chances to seal the points.
First, Currie crossed to the far post, Alan Lee headed it back and an unmarked Richards steered a six-yard header over the top, before promptly being replaced by Danny Haynes.
It was Haynes who had the other golden opportunity, again from a Lee knock-back off a Fabian Wilnis cross, but although the forward made decent contact from close range, Marshall pulled off a reflex save to divert the ball over the bar.
Millwall saw that as a sign that there may be something for them and they then continued to force the pace for long spells, with Ipswich seemingly happy to soak it up and try and hit on the break.
For all their possession, the Lions created very little until they snatched an equaliser with just five minutes to go through skipper Livermore.
Dunne's corner was headed back into the centre where Elliott out-jumped keeper Supple only to see his header cleared off the line by Jason De Vos, but Livermore returned it with interest over the heads of the covering defence to find the net.