In-form striker Vaughan thought that he had levelled for the home side just before half time, but his goal was ruled out for offside.
Craig Cathcart had a chance to double the lead for Blackpool on the hour mark, but just headed over from Thomas Ince's corner.
Following Cathcart's miss, Huddersfield went on the counter-attack, as Duane Holmes burst through midfield before passing to Vaughan, who caught the ball on the half-volley to make it 1-1.
The striker appealed for a penalty three minutes later when he tangled with Cathcart inside the box, but the referee dismissed his shouts.
Oliver Norwood tried an ambitious shot from 25 yards out with just under 15 minutes left to play as Mark Robins's side pushed for a winner, but a poor connection with the ball saw it clear the crossbar.
Huddersfield had another chance to score on the break inside the last 10 minutes, but Holmes was brought down inside the box by Angel Martinez, who was shown a red card for the tackle.
Vaughan stepped up to take the spot kick, smashing it towards the centre of the net, but he got too much of his foot under the ball, resulting in his effort striking the crossbar.
A frantic final five minutes saw chances at both ends of the pitch, but neither team was able to find the winning goal.