© PA Photos
Orient thought they had taken the lead after 21 minutes, but Dave Mooney's strike was ruled out for offside.
Hull then took the lead on 41 minutes through Nick Proschwitz, who controlled expertly before smashing the ball past the goalkeeper.
The O's had the ball in the net for the second time, but Lee Cook's effort was ruled out for offside.
Dean Cox then grabbed a late equaliser with three minutes left when Dean Cox's floated cross dipped under the bar to make it 1-1.
© PA Photos
Neither side could find a late winner and the game headed into extra time.
Proschwitz won possession deep inside the O's half just after the restart, forcing the defence back before hitting his shot straight at Jones.
The League One side instantly came back with an effort of their own, but Mooney's shot from the edge of the area was easily gathered.
Orient had a big chance to grab the winner in the second half of extra time, though the pressure on Michael Symes forced him to head over.
In the 117th minute, Proschwitz crossed the ball which was cleared only as far as Tom Cairney, who fired home with a left-footed strike to secure the Tigers' place in the FA Cup fourth round.