Simon Grayson's side dominated possession and created a string of chances but it looked like it would not be their day until Vernon's intervention seven minutes from time.
It started promisingly for Blackpool with Andy Morrell shooting just wide after a clever through ball from Wes Hoolahan.
Keigan Parker then saw a goal chalked off for offside after a clever through ball from former Swan Adrian Forbes inside the first ten minutes.
But Swansea hit the hosts with a sucker punch in the 20th minute when a corner from Lee Trundle was flicked off the head of young left-back Carl Dickinson at the near post and flew past keeper Rhys Evans to nestle in the corner of the net for an own goal.
But that didn't put Blackpool off their stride and they continued to create opportunities with Ian Evatt particularly profligate in front of goal, missing narrowly after two set pieces by Hoolahan.
Swansea's concern showed in the second half which was only three minutes old when keeper Willy Gueret was shown a yellow card for some rather silly time-wasting.
Blackpool managed to get the ball in the net again early in the half when Gueret palmed away a powerful Keith Southern shot and half-time substitute Ben Burgess pounced to turn the ball into the empty net only for the strike to be ruled out for offside.
Moments later Blackpool again came close to levelling the scores when good work from Parker put in Hoolahan whose powerful shot from the edge of the area bounced off the underside of the crossbar and somehow stayed out of the goal.
Blackpool were rarely threatened at the other end, although Lee Trundle did get in behind the defence a couple of times only to see Evans beat him to the ball.
But it looked like the one goal would be enough until the 83rd minute when a clever pass by Hoolahan put Vernon in behind the visiting defence and the striker, who has faced a frustrating time on the bench in recent weeks, slotted the ball through Gueret's legs and into the net.
That seemed to wake Swansea up and Andy Robinson lifted a free-kick just over the bar, although the best chance to seal victory fell to Hoolahan who turned Kevin Amankwaah inside out but chose to shoot rather than picking out a pass and saw his effort comfortably saved.