Boro took the lead on 73 minutes through Mark Viduka but Hull fired back six minutes later through substitute Nicky Forster to ensure both sides will be in Monday's draw for the fourth round.
Middlesbrough pushed forward early on and created a chance when Viduka found himself with room for a shot but his right-footed effort from 18 yards was comfortably saved by Boaz Myhill.
The visitors came close to breaking the deadlock midway through the half when Yakubu raced into the box and tried to jink the ball past Myhill, but the Hull keeper got enough on the ball to allow Sam Ricketts to clear for the Tigers.
Boro came even closer seconds later as Stewart Downing swung in a pin-point cross from the left which beat Myhill and left Yakubu with an easy finish from three yards, but the Nigerian failed to convert as the ball flew up off his knee and the Hull defence pounced to clear.
Jon Parkin created a chance for himself towards the end of the half as he got around the back of the Middlesbrough defence and fired in a shot from the left-hand side of the box, but Bradley Jones did well to turn the ball over the bar.
Stuart Elliott tested Jones just before the break as the Hull man's looping header from 12 yards forced the Boro keeper to scramble back and tip the ball wide for a Hull corner.
Middlesbrough came close early in the second half as Danny Coles brought down Yakubu just outside the box, and Downing took the resulting free-kick which he curled left-footed towards the top corner, but Myhill was equal to it as he managed to turn the ball over the bar for a corner.
The visitors broke the deadlock on 73 minutes when the ball fell to Viduka inside the box and he had enough time and space to slam the ball right-footed past Myhill to put his side into the lead.
Hull fired back on 79 minutes when David Livermore curled in a free-kick from the right onto the head of substitute Forster who put it neatly into the back of the net from close range to level the scores.
Middlesbrough sub James Morrison came close to putting his side back into the lead moments later but his right-footed effort from 12 yards was well turned away by Myhill.
Myhill was called into action again late on as he managed to turn Chris Riggott's powering header onto the post allowing the Hull defence to clear.