Foster handed Pierre-Emerick Aubameyang his 23rd goal of the season and allowed the Gunners to block his kick and score.
And then the Hornets captain Deeney made sure that Arsenal won a win that saw them overtake Manchester United and Chelsea and return to fourth in the Premier League, as he was stupidly expelled a minute later. for giving Lucas Torriera an arm.
The hero of the FA Cup semi-final Deeney tore his shirt off in disgust and seemed to have the words with the Arsenals dug as he walked away in the 11th minute. But the damage had been done – and the Gunners had their sixth championship win in the league, and their first clean sheet.
Foster took his hands and admitted, "I said sorry to the boys. They were brilliant.
"I should have just Cruyffed him. I tried to pass him off but before I knew it he was damned on me.
"I have to do it faster. You have to get rid of it as quickly as possible, even if it goes in the Z line. They can't score from the Z line. It's fast. Lesson learned."
On Deeney's red card he said: "Troy isn't happy and says it's nothing."
Watford manager Javi Gracia said: "I am proud of my players. I think it is a yellow card, but never red. Troy is very sad. We are a team."
The Gunners' rival Unai Emery admitted: "The red card helped us, but the three points are very important. A clean sheet is also very important."
When Arsenal lost 2-1 to Vicarage Road last season, Deeney accused them of lacking "cojones". He could have cared more about his forearm Tuesday night than worrying about parts of the Arsenal anatomy.
Chief Watford Javi Gracia and Gunners leader Unai Emery were old teammates along with their playing days at Real Sociedad. When Emery was offered the work of the Arsenal last summer, he asked Gracia for his opinion, and the couple had dinner together.
Even so, Emery would not have expected this kind of help.
The Gunners started nervously while goalkeeper Bernd Leno cut his throw-in under Andre Gray's pressure.
But then an extraordinary double disaster for the Hornets, in the space of a minute. First, Foster, remembered after Heurelho Gomes' FA Cup heroism last week, failed disastrously. He took the passe-dale of Daryl Janmaat, and fatally dallied.
Aubameyang closed it from behind without being seen, and ran to block Foster's kick, which flew into the net.
Less than a minute later, Watford was ten men. Deeney went into a challenge with Torriera and seemed to throw a forearm in his face. The Uruguayan went down, the linesman Richard West beat the flag, and referee Craig Pawson, to Deeney's astonishment, produced the red card. Deeney, a hero at Wembley last week, had destroyed his team's hopes.
Aubameyang then pulled to the side before Watford reacted with a gunshot while Craig Cathcart saw Leno push his shot on the post and off.
But the Arsenal had the numbers now, and when Alex Iwobi shot, Foster redeemed himself in part with a nice parade. Watford was still bypassing the chances though, and Etienne Couple forced a brilliant save for Leno with a curved free kick.
Alexi Iwobi's cross-shot was a whisk away as the Arsenal continued to probe, and he went through and Henrikh Mkhitaryan seemed confident of scoring, only to see Foster somehow stop his volley shooting point.
To their credit, Watford never gave up, and the Gunners had their main escape while Adam Masina let fly for 30 yards and saw that his shot could not be canceled.