Thomas Tuchel's side were far from their efficient best at Vicarage Road but had enough attacking quality to emerge with three points and stay ahead of Manchester City and Liverpool.
Not that Tuchel took a great deal of satisfaction from the result – the German not holding back in his assessment.
"We were lucky. We should admit it," Tuchel said. "Sometimes you need it. Today we could not reach this level. We were not ready for this game. We are to blame.
"We never found the right attitude. It was a big exception from the rule. We conceded a lot of chances in the first half and did not create much. We were very lucky to escape with a win."
After a 32-minute suspension, while a fan who had suffered a cardiac arrest was treated by emergency services, Chelsea took the lead when Mason Mount coolly converted after a well-worked move in the 29th minute.
But Watford deservedly levelled before the breakthrough Nigerian Emmanuel Dennis.
Ziyech came on for injured defender Trevoh Chalobah on the hour and struck the winner 12 minutes later with the outstanding Mount turning provider.
Chelsea lead the standings with 33 points from 14 games, with City on 32 and Liverpool on 31.
Claudio Ranieri's side will take heart from the way they pushed the league leaders but are just one place and three points above the relegation zone.
"We deserved at least a point but that's football," former Chelsea boss Ranieri said. "I'm very satisfied with our performance. Sooner or later the points will arrive."
Tuchel made six changes from the side that drew with Manchester United at the weekend and Chelsea looked disjointed for much of the evening.
Watford were the better team either side of the suspension but fell behind to Chelsea's first move of real quality.
The ball was played to Marcos Alonso down the left and he slipped it into Kai Havertz who shifted it across to the unmarked Mount who had time to pick his spot.
Watford responded well with Danny Rose testing Edouard Mendy with a powerful shot. Chelsea continued to stutter and when Ruben Loftus-Cheek lost possession in midfield, Moussa Sissoko powered forward and picked out Dennis whose shot took a deflection on its way past Edouard Mendy.
The hosts could have been ahead with Mendy making a fine save and Sissoko scuffing a decent opportunity.
Watford continued to look a threat in the second half but Chelsea gradually began to assert some control and the quality they have on their bench eventually told as Ziyech came on to secure the points with his first league goal of the season.
Mount, Chelsea's best player, was played into space down the left and his precise low cross was met by Ziyech whose powerful first-time shot beat Watford keeper Daniel Bachmann for pace.