The visitors had the first opening of the game when McGugan found space to run at goal and drive an effort towards the net, but his strike went just over the bar.
The Owls came close to taking the lead when McGugan ran down the right flank and directed a cross into the box for the run of Atdhe Nuhiu, only for the striker to guide his close-range header over the bar.
In the second half, the Owls took the lead when they won a free kick down the left and McGugan's delivery evaded the head of every player in the penalty area and nestled past Parish into the bottom corner.
Nuhiu came close to doubling his side's advantage minutes later as Tom Lees knocked the ball into his path from a corner, but the striker was denied by a good save at his near post by Parish.
Blackpool pushed to get back into the game late on and Grant Hall headed an effort just wide of the post from a free kick, but they could not get the breakthrough as the Owls held out for the three points.