The Owls had dominated for long spells but only had Chris Maguire’s first-half penalty to show for their efforts.
The 39th-minute spot-kick came after Peter Clarke was adjudged to have fouled Stevie May, Maguire subsequently sending Joe Lewis the wrong way from the spot.
Lewis denied the Owls on several occasions, including a sprawling dive to thwart May, and Wednesday looked like they could be punished for their spurned chances.
Ishmael Miller had punched the ball into the net, earning a booking for his troubles, before finding himself three yards out with just Westwood to beat.
But somehow the Republic of Ireland goalkeeper blocked the point-blank header to stun Miller, who to add insult to injury was sent off in stoppage time for a second yellow card after a foul on Tom Lees.
Westwood’s heroics earned Wednesday only their third home Championship win, much to the relief of head coach Gray.
“It just shows with us that we just cannot get the second goal, to take the pressure off us,” said Gray.
“Myself and the fans should have been enjoying the last 10 minutes. I thought we dominated the ball.
“We had great opportunities to pick them off, and get the second goal. I thought Stevie May was unlucky with his header, it was a great save.
“Again we are relying on Keiren Westwood to pull off a fantastic save and give us two points. I don’t think he had a touch of the ball apart from his distribution. It’s about concentration levels, it was a fantastic save.
“That’s probably the best save he has made this season. The reason why I say that is because he has had very little to do in the game.
“I was disappointed that they got in so easily because I have a balance down the left in Joe Mattock, Claude Dielna and Jeremy Helan.
“The cross comes in and I am sure the centre-forward is beating himself up thinking ‘how did I not score?’.
“But credit to the lads; a clean sheet and, like I said before the game, it was a must-win game.
“That’s all we could do (yesterday),” added Gray, following back-to-back defeats against Wolverhampton Wanderers and Fulham.
Maguire and May linked well after being paired together in attack and both could have netted in a 60-second spell in the second half. First Maguire’s drilled cross from the left was deflected onto the crossbar before May’s free header blazed over from eight yards out.
Sheffield Wednesday: Westwood, Palmer, Lees, Dielna, Mattock, Drenthe, McGugan (Lee 79), Semedo, Helan, Maguire, May (Nuhiu 85). Unused substitutes: Lavery, McCabe, Zayatte, Maghoma, Kirkland.
Blackpool: Lewis, McMahon, Daniels, Clarke, O’Dea (Dunne 80), Eagles, Perkins, O’Hara, Murphy (Mellis 52), Davies (Delfouneso 28), Miller. Unused substitutes: Parish, Lundstram, Waddington, O’Keefe.
Referee: J Adcock (Notts).