The Tigers certainly deserved to take something away from the match and could count themselves a shade unlucky not to have won the game.
Derby were unconvincing, particularly at the back, but they always have enough quality to damage the opposition and their opening goal was a case in point. Hull had battered their goal before Stephen Pearson embarked on a 70-yard run that set up Gary Teale for the opening goal.
Hull responded with a superb Andy Dawson free-kick to equalise, but a rare moment of defensive slackness allowed Darren Moore to restore Derby's lead in first-half stoppage time.
The second half was as even as the first but Derby were caught with two minutes remaining and Livermore gave the Hull supporters a happy end to what had been a good advert for the Championship.
Derby will look back and see this as a missed opportunity and their hopes of equalling two club records also slipped away.
They were chasing a sixth consecutive clean sheet for the first time in almost 95 years but that had gone by half-time and the prize of a ninth straight victory disappeared when Livermore volleyed home.
But they remain in a strong position at the top of the table and will come across less accomplished teams than Hull between now and the end of the season.
The visitors played the ball around with confidence and Nicky Forster gave Moore some uncomfortable moments with his ability to run at defenders.
Derby's best moments tended to involve Teale and the winger took his goal well when Pearson sprinted away down the left to deliver a low cross that the former Wigan player steered into the bottom right-hand corner from eight yards.
Hull had earlier seen six attempts at goal blocked but they were rewarded when Dawson curled a left-foot free-kick over the wall and into the top left-hand corner to level.
The game was drifting towards half-time when a corner allowed Moore to place an unmarked header across goal and inside the left-hand post as Hull froze.
They would have been disappointed to concede so easily but they continued to play with spirit and thoroughly deserved the late equaliser that was so cleverly constructed.
Sam Ricketts combined cleverly with Forster and the full-back produced a dangerous cross from the right touchline that Livermore gleefully hooked into the roof of the net to deny Derby another three points.