Their win maintained Watford's separation from the relegation pack and left the home fans believing that safety may only be another two victories away.
A remarkable late equaliser nearly arrived deep in stoppage time as Pickford charged up for a corner and headed into the path of Dominic Calvert-Lewin, but the substitute could not scramble the ball in as Everton's miserable away record extended to one win from 22 top-flight games.
No team has conceded more top-flight home goals than the 26 Watford have shipped, and when Oumar Niasse inadvertently hit the woodwork in the first half, the Vicarage Road crowd would have been forgiven for expecting another hard examination for their defence.
Watford's new head coach Javier Gracia wasn't about to denigrate Everton's poor performance.
"It was a very tough game".
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"I was pleased with the overall performance, but in the final third we could have done a lot more". We've got West Brom next week and there's no point winning one and losing three or four.
"Troy is very important to us on the pitch and out of the match".
Speaking to BT Sport, he said: "I'm not remotely bothered".
One player who has impressed Allardyce is Oumar Niasse.
Each side wasted headers early in the second half.
Sebastian Prodl and Michael Keane each wasted opportunities after the restart, both defenders heading off target at either end as the game became slightly more open.
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The following two tabs change content below. A swift turn and a powerful strike did the rest.
For Allardyce, the difference was Deeney. It was a bad goal to give away at that stage.
"I think Oumar's position at Everton has never really been as good as it is at the moment", Allardyce said.
The best chance of the first half fell to Everton's Oumar Niasse whose shot from a tight angle in the 12th minute was tipped onto the post by Orestis Karnesis.
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