Watford moved out of the relegation zone as their stunning revival under new manager Nigel Pearson continued with a 3-0 victory at south coast strugglers Bournemouth on Sunday.
Bournemouth offered little by way of a response and substitute Roberto Pereyra completed the rout in stoppage time.
The win, Watford's fourth in the six games since Pearson took charge with them bottom of the table, lifted them to 17th place, ahead of Aston Villa who play Manchester City later.
Pearson, who inspired Leicester's escape from relegation in 2014-15, has collected 13 points from his six matches at the helm, five more than his predecessors Javi Gracia and Quique Sanchez Flores, both sacked this season, managed between them.
"He has stripped it back to basics," Watford captain Deeney said. "I don't want to be too simplistic because that doesn't do him enough credit. He puts demands on the players and the players have accepted those demands."
While Watford, who won only one of their opening 17 league games and were six points adrift at the bottom heading into Christmas, are on the up, Bournemouth's hopes of a sixth successive season of top-flight football are sinking.
Eddie Howe's side looked short on confidence as they slipped to their third successive defeat without scoring a goal.
They are second bottom with 20 points from 22 games having been as high as seventh in early November.
Howe has won plaudits for the passing style Bournemouth have used to punch above their weight in the top flight, but there are signs that it is becoming their Achilles heel.
They were often guilty of careless passing as they tried to play out from defence and were lucky not to be punished early on when Gerard Deulofeu forced a smart save from keeper Mark Travers, making his first Premier League start.
Bournemouth did not learn their lesson and when Travers played a loose pass out in the 42nd minute, Watford stole the ball and Ismaila Sarr's cross fell to Doucoure to finish well.
Sarr was involved again for Watford's second in the 65th minute when his cross was diverted to Deeney who thumped a first-time shot past Travers.
Deeney could have added to his tally as Bournemouth wilted and Pereyra's fine finish rounded off a great day for Watford.
Since beating Manchester United on Nov. 2, Bournemouth have taken four points from their last 11 matches and unless Howe can stop the rot they are heading for relegation.
"The manager always has to take responsibility when things aren't going well," Howe said. "Instilling confidence back to the players is my job."