Hull's record crowd since their move to the Kingston Communications Stadium were kept on the edge of their seats throughout the game.
It looked like the match was going in Doncaster's favour until the double sending off in the 82nd minute of Hull's ex-England striker Nick Barmby and Rovers midfielder Jermaine McSporran.
McSporran was dismissed for a second yellow card while Barmby collected a straight red card for retaliating against the Doncaster player.
Tigers boss Peter Taylor said: "Nicky is very disappointed and I shall be looking at the video. He says he did nothing."
However, the referee thought that Barmby had tried to butt his opponent.
In the last few minutes both teams pressed for victory and Doncaster were badly caught out when Hull broke away for Elliott to claim the spoils.
Rovers equalised in first-half stoppage time when they won a free-kick just outside the area and Dave Mulligan scored.
The second half was wide open with chances coming thick and fast at both ends.
Just before Elliott's winner, Hull goalkeeper Boaz Myhill made a great save to deny Simon Johnson and afterwards he preserved Hull's lead in some desperate penalty area moments, including a tremendous block to deny Paul Green.