Hull City striker Jon Parkin looked to have sealed the points for the visitors when he pounced 13 minutes from time, but captain Livermore was on hand on 81 minutes to rifle home a 25-yard leveller to earn the Lions a share of the spoils.
Millwall played most of the game with ten men when Paul Robinson was sent off on 35 minutes for a professional foul on Craig Fagan, but Hull never really capitalised on their advantage.
The first real opening fell to the visitors when Lions striker Ben May's misplaced pass allowed John Welsh to set Fagan away. But the lively striker tried one trick too many and Zak Whitbread recovered well to deny Fagan a shot.
Millwall's first effort came in the tenth minute when Berry Powel raced on to a long clearance by Andy Marshall, only to drag his shot across the face of the goal and out for a throw.
Powel's presence began to unsettle the Hull back line and he was again involved moments later when Millwall went agonisingly close to opening the scoring.
Powel flicked on another Marshall long clearance before teeing up strike partner May. He found space on the edge of the area but saw his well hit shot sail just wide of the left-hand post.
The home side continued to pile on the pressure and Marvin Elliott had another long-range effort tipped round the post by Boaz Myhill, before midfielder Jody Morris nearly gifted the visitors the lead. His misplaced pass in the centre circle on 14 minutes allowed Fagan to nip around Paul Robinson and have a free run on goal. But the former Birmingham and Colchester striker's toe poke past keeper Marshall went the wrong side of the post much to the relief of Morris.
Fagan was again involved as he this turned provider for partner Parkin. Fagan found space down the left on 26 minutes and crossed and Parkin who shot narrowly wide from 12 yards.
Leon Cort then forced keeper Marshall into a smart save when the home side failed to clear Damien Delaney's long throw. The former Millwall trainee's rasping volley from the edge of the area looked destined for the bottom corner before the outstretched arm of Marshall turned it around the post.
But the home side were reduced to ten men on 35 minutes when Robinson failed to contain Fagan. The striker's pace again saw him run clear of the Millwall backline before he was hacked down by Robinson who, despite being injured and thrown on to a stretcher, was shown a red card by referee Lee Probert.
From the resulting free kick Stuart Elliott dragged his left-foot shot just wide of the right-hand post.
In an uneventful second half, Hull finally made a breakthrough 13 minutes from time when Keith Andrews picked out Parkin to fire in from eight yards.
But their joy was short lived as just five minutes later, Livermore latched on to Ben May's knockdown to fire in an unstoppable 25-yard shot to earn Millwall a point.