The Blues looked set to hand their title rivals a boost by dropping points for the third time in four games, but substitute Ziyech made a decisive impact in the 72nd minute.
Mason Mount gave Chelsea the lead after play was suspended for around half and hour when a fan suffered a cardiac arrest in the stands. Watford later confirmed the individual had been stabilised.
Emmanuel Dennis equalised before half-time but Mount teed up Ziyech for his first Premier League goal of the season to remove the threat of Thomas Tuchel's men being overtaken by Manchester City or Liverpool.
Watford started brightly and Edouard Mendy had to react quickly to stop Cesar Azpilicueta scoring an own goal in the fifth minute, but there was a significant break in play when a spectator fell ill.
The thoughts of everyone at Chelsea Football Club are with the fan and all those affected.— Chelsea FC (@ChelseaFC) December 1, 2021
Our thanks to the medical staff here at Vicarage Road for their quick response. 💙 https://t.co/8LK5JaKOZp
Chelsea's first effort was cracked against the post by Mount shortly after play resumed but he did not fail at the second attempt, guiding home Kai Havertz's pass in the 30th minute after an exquisite touch from Marcos Alonso.
Watford drew level on the stroke of half-time, with Moussa Sissoko dispossessing Ruben Loftus-Cheek and launching a break that ended with Dennis finding the bottom-left corner with the help of a deflection off Antonio Rudiger.
Tuchel hooked Saul Niguez and moved Trevoh Chalobah into midfield for the second half but a hamstring injury meant he had to be replaced by Ziyech in the 60th minute.
The game appeared to be heading for a draw until Mount picked out Ziyech in the centre of the box and the Morocco international's first-time effort had too much power for Daniel Bachmann to keep out.
Bachmann did well to stop Ziyech doubling his tally in the closing stages but Watford were unable to come back a second time and salvage a result.