Newcastle were the better side in the first half at Vicarage Road and deserved the lead given to them when Dwight Gayle turned in Federico Fernandez's flick from Matt Ritchie's corner in the 23rd minute.
Watford, who hit the post through Danny Welbeck, were indebted to a vital save by Ben Foster from Allan Saint-Maximim before the break - leaving them in position to mount another recovery in the second half.
They were handed a lifeline after 52 minutes when Deeney drilled home a spot-kick following Ritchie's foul on Kiko Femenia, and he repeated his heroics nine minutes from time after Javier Manquillo hauled down Ismaila Sarr in the box.
It gave Watford a priceless three points as they showed the same powers of recovery that saw them overturn a 1-0 deficit to beat doomed Norwich City in their previous home game - and crucially leaves them six points clear of Bournemouth in the bottom three, although the Cherries have played a game less.
"I understand that those blockages can come in and affect performance. What was important was that we were able to find the answers. It's never easy. I've been in that situation as a player, it can be very stressful and you have to perform.
"We've had a difficult season. When players are dealing with disappointment on a regular basis it's hard to go out and play with confidence. What we need is the commitment to have a positive intent and I really applaud the players for how they turned that round. Before this last week we'd not won from a losing position and they've done it twice this week.
"We have to keep focus, don't think the job is done. We are working hard - back in December it didn't look possible but throughout it all we have tried to remain positive. You've always got a better chance if the collective is stronger than the individual.
"Troy Deeney is someone who embraces pressure, he does not shirk responsibility and good for him. I am pleased for him today. Our job isn't finished yet."