The home side had dominated the first half and appeared to have taken an eighth minute lead only for referee Fred Graham to rule that Mark Allott had knocked the ball over the line with his hand.
Allott was booked, the first of a number of cards flashed by the Essex official, who also ordered Chesterfield manager Roy McFarland into the stand for protesting too loudly at one of his decisions.
By then Chesterfield had seen Niven sent off when he tripped Nick Barmby in the 54th minute, but the visitors were unable to make the extra man work in their favour.
It was the home side who did most of the pressing but Hull defended well and got the breakthrough from a set-piece 16 minutes from the end.
Damien Delaney headed the ball back across goal and Lewis hooked a right-foot shot into the roof of the net from eight yards.
That promised to be enough to put Hull on top of League One but Myhill made a serious error with eight minutes remaining.
He came to punch an inswinging corner from Shane Nicholson but only succeeded in helping the ball into his own net.
Hull were shattered but it was the least Chesterfield deserved for a spirited and not stop performance.
They were the better side before the break even though Hull striker Aaron Wilbraham struck the bar and they pushed the promotion favourites back for much of the game.
It was a hard fought contest and the only sour note was the performance of the referee who at times baffled both teams with some of his decisions.