Cleverley had not long been on the pitch when he netted his first goal in more than a year in the 74th minute at Selhurst Park.
Palace manager Roy Hodgson brought on Christian Benteke for his first appearance in four months following an injury lay-off, but the striker could not produce an equalizer.
Watford is seventh in the standings, six points behind Manchester United, which is at Tottenham on Sunday. Palace is 14th, four points above the relegation zone.
Source: Fox Sports