Craig Cathcart's own goal after 38 minutes had Palace on course for victory, but the Watford defender scored at the right end 23 minutes from time.
And Cleverley, yet to start in the league this season as he returns from injury, netted his first goal since October 2017 with a superb volley to give his side, who only managed two shots on target, an impressive victory.
Watford's triumph halts a troubling run that had seen them win only twice in their last 11 top-flight games, while Palace have only won two of their 11 home matches this season.
Inside three minutes, Watford incredibly hit the woodwork twice in the same move. Gerard Deulofeu nutmegged James Tomkins and fired an effort from 12 yards against the same post that Roberto Pereyra struck from the rebound when he appeared destined to score.
The visitors, who lost Will Hughes to a head injury, saw captain Troy Deeney send a header just wide, while Tomkins had an aerial effort of his own tipped over by Ben Foster at the other end, leading to a corner from which Palace took the lead.
In one of the scrappiest goals of the season, Tomkins attempted to turn in Luka Milivojevic's corner from close range, and Abdoulaye Doucoure's attempted clearance bounced in off the unfortunate Cathcart.
It was Palace's turn to lose a player to injury on the stroke of half-time, Wayne Hennessey replacing Vicente Guaita, but Foster was the keeper who had to keep out a Milivojevic effort, which the hosts claimed had bounced off Adrian Mariappa's hand.
Wilfried Zaha raced clear to create a glorious chance for himself after the break, but he was denied by Foster, who also made a fine stop to keep out an audacious 30-yard attempt from Milivojevic.
Yet just as Palace looked like finding a result-clinching second goal, Cathcart scored at the right end, heading in Jose Holebas' corner at the far post with Hennessey caught out badly by the delivery.
James McArthur somehow failed to turn in Zaha's cross-shot for Palace, while Watford saw Deeney's deflected effort hacked off the line by Aaron Wan-Bissaka, with the match in the balance until it was settled 16 minutes from time.
Cleverley – just six minutes after coming on – was the scorer, sending a sweet volley from 15 yards into the top corner, Palace having twice failed to clear a corner.
What does it mean? More home woe for Palace
Palace came into the game with some momentum after their away win at Wolves, and a run that had seen them lose just once in five Premier League games.
But their home form remains a big problem. Just two wins and six goals in 11 top-flight games at Selhurst Park is not enough, and the main reason Roy Hodgson's men remain 14th and now sit just four points clear of the bottom three.
Watford, meanwhile, are up to seventh in the table, and continue to pick up enough wins to stay firmly in the mix to finish as best of the rest outside the Premier League's big six.
Cathcart & Foster crucial
Cathcart could do nothing about his first-half own goal, but made up for it with a firm second-half header to bring Watford level, as well as making six defensive clearances at the other end.
Foster also impressed, making six saves, including pivotal stops from Zaha and Milivojevic to keep Watford in it at 1-0 down.
Horror show for Hennessey
Hennessey has been in the news for the wrong reasons over recent weeks, having to deny he was making a Nazi salute in a picture that emerged after the FA Cup win over Grimsby Town. He would not have expected to play in this one, and he struggled when replacing Guaita, He was caught out of position for Cathcart's goal and ended up without a save.
Key Opta Facts
- Crystal Palace have lost six of their 11 home Premier League matches this season (W2 D3), only one fewer than they lost during the entirety of the 2017-18 campaign (7).
- Watford are unbeaten in four away Premier League matches (W2 D2), their best run since September 2017 (also four unbeaten).
- No player has scored more Premier League own goals this season than Watford defender Cathcart (2, level with Wesley Hoedt).
- Watford’s Craig Cathcart became the first player to both score a goal and an own goal in the same Premier League game since Ryan Shawcross in December 2017 (Stoke v Tottenham).