Both teams had chances throughout the contest, but the main talking point came in stoppage time, when Wednesday attacker Fernando Forestieri was controversially handed a second yellow card for simulation.
It took until the 15th minute for either side to come close to scoring, with the opportunity arriving for Wednesday. Barry Bannan's strike towards goal appeared to be causing little concern, but Hull stopper Allan McGregor had to be at his best following a deflection from Tigers centre-back Curtis Davies.
McGregor was again called into action just before the 30-minute mark to keep out a swinging free kick from Forestieri. The Wednesday midfielder came even closer 10 minutes before the break, however, when his powerful strike from distance thundered off the crossbar.
Hull ended the first period having had more than 60% of the possession, but it was the visitors that looked the more likely to make the breakthrough in the opening 45 minutes of action.
Mohamed Diame came close to sending the home side ahead early in the second half, but his strike from the edge of the box was deflected just wide.
Hull had another chance in the 52nd minute when Sam Clucas went though on goal, but his effort was just wide of the post, before Westwood kept out a strike from Abel Hernandez, who grew into the match.
Clucas came even closer in the 65th minute when he curled one towards the bottom corner, but he hit the outside of the post and it would not fall for Hernandez, who was in close proximity.
Hernandez's best chance of the match came 10 minutes from time when the ball fell for the striker inside the box, but Westwood was again on hand to make the save.
Wednesday were reduced to 10 men in stoppage time when Forestieri controversially picked up a second yellow card for diving, but Hull could not make use of their numerical advantage late on as the points were shared in the Championship clash.
The result has moved Hull two points clear of second-placed Burnley in the table, while the visitors remain in sixth spot.