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The New Zealand international thought he had doubled his tally in the 28th minute when he converted from Knockaert's deflected shot, but the striker had strayed into an offside position.
Wood continued to cause problems throughout the first half and had an appeal for a penalty turned down in the 34th minute after being bundled over by Gabriele Angella.
Polish defender Marcin Wasilewski headed narrowly over the bar in the 43rd minute as Leicester continued to dominate proceedings.
Knockaert doubled Leicester's lead eight minutes after the break. Jeff Schlupp drove at the Watford defence and wriggled past the challenge of Lloyd Doyley before pulling the ball back to the midfielder, who rifled the ball in at the near post.
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David Nugent could have sealed the game for the away side just two minutes later, but he headed well over the bar from 12 yards.
Watford started playing their best football after falling two goals behind, and Diego Fabbrini and Ikechi Anya combined well to set up Fernando Forestieri, but the Argentine fired his 12-yard shot straight at Schmeichel on the hour mark.
The trio combined once more two minutes later, but Anya was the guilty party this time as the Scottish international blazed his shot over the bar from close range.
The home side continued to waste good chances as Troy Deeney couldn't stretch enough to convert Anya's right-wing cross and the striker's effort flew inches wide of the post.
In contrast, the visitors were clinical and Lloyd Dyer wrapped up all three points in the 86th minute when his shot bounced into the net despite Almunia getting a strong hand onto the winger's shot.