The Lions came into the clash unbeaten in four matches following a disappointing start to the season and looked to be heading for three more points after Carl Asaba prodded them in front on the hour mark at the KC Stadium.
Millwall had started the brighter of the two sides and after Barry Hayles had worked his way into the box the ball fell to Don Hutchison who crashed a shot inches wide of Boaz Myhill's left-hand post.
At the other end it was another veteran who should have broken the deadlock as Nicky Barmby latched on to a long kick by the keeper only to lash an early shot over the crossbar.
After the interval it was again Millwall who looked the more likely to score as a header by Alan Dunne from a pin-point Philip Ifil cross was clawed away by the City keeper.
But the relief was only momentary for Hull who are struggling to adapt to life in the Championship as Asaba was on hand to slam home the rebound with the keeper stranded on 61 minutes.
With time running out and the Tigers looking devoid of attacking ideas, manager Peter Taylor sent on the powerful Burgess in a last throw of the dice.
And the big striker duly delivered as he latched on to a raking left-wing cross from Andy Dawson to rescue a point with a firm header from six yards.
The result moves the Tigers up to 14th place in the Championship table while Millwall remain just clear of the bottom three on goal difference.