Watford faced an uphill battle in trying to rally against Jose Mourinho's men but nearly pulled it off, with Andre Gray scoring in the 65th minute and De Gea coming up with a remarkable save to deny a header by Christian Kabasele in second-half stoppage time.
Despite the home loss, Watford (4-0-1) is still in fourth place in the Premier League with 12 points after five matches, just three behind first-place Chelsea.
Manchester United is provisionally in eighth place with nine points.
In other results, Liverpool beat Tottenham 2-1, Manchester City routed Fulham 3-0, Bournemouth outgunned Leicester City 4-2, Arsenal edged Newcastle 2-1, Crystal Palace topped Huddersfield Town 1-0 and Chelsea trounced Cardiff 4-1.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)