The Blues, who lost 3-0 at home to Bournemouth last week, were woeful again at Vicarage Road and had Tiemoue Bakayoko sent off inside half an hour.
Troy Deeney scored a penalty in the closing stages of the first half, but Chelsea stayed in the contest and equalised through a magnificent Eden Hazard goal.
The visitors were not level for long, however, as Daryl Janmaat scored his own memorable effort to put Watford back in front, before Gerard Deulofeu, man of the match on his home debut, and substitute Roberto Pereyra rounded off the win with breakaway goals to secure an emphatic win.
Conte had called on Chelsea’s hierarchy to “prepare a statement... to say they trust me in my work” ahead of the game, but it was another dismal evening for the defending champions, who are now 19 points adrift of leaders Manchester City.
Inevitably, Conte was asked about his future in the post-match press conference.
“My position? It is the same,” he said. “I stay here, try to work and put all myself in the work.
“The pressure? Which pressure? What is the pressure?
“I work — if this is enough it is OK. Otherwise, the club has to take another decision.
“We performed very bad but maybe I made the mistakes with the starting XI today.
“My choice was very poor I think. It was very difficult to change something tonight.”
Michy Batshuayi and Diego Costa scored the goals in a 2-1 win for Chelsea here last season. That was the second game of a campaign which ended in Premier League glory for the Blues but, like those goalscorers last August, Chelsea’s hopes of retaining their crown are gone.
Either of those strikers would have had a chance of playing here, as Conte once again deployed Hazard as Chelsea’s main attacking option with new signing Olivier Giroud warming the bench.
Deulofeu was lively in the early exchanges and sent a shot into Thibaut Courtois’ side-netting after being picked out inside the box.
Bakayoko was enduring another dismal display in a Chelsea shirt and was booked for bringing down Etienne Capoue inside the Chelsea half before Pedro hit a post on a rare Chelsea foray forward - only to see a free-kick given for handball against Victor Moses in the build-up.
The challenge became harder for Conte and his players when Bakayoko’s evening came to an abrupt end as a second yellow card for a crude foul on Richarlison saw him dismissed by referee Mike Dean.
It continued to go from bad to worse for the Italian as Dean awarded a penalty to the hosts when Courtois burst from his line to close down the onrushing Deulofeu, with the Barcelona loanee going down under minimal contact.
Deeney, whose only previous league goals this season were penalties against Arsenal and Manchester United, stuck home the resulting spot-kick to give the Hornets a deserved half-time lead.
Chelsea were brighter after the restart, but the numerical advantage often helped Watford out and they soon started to create chances, Deulofeu curling a shot wide before David Luiz, booked moments earlier, gifted possession to the hosts only for Richarlison to also narrowly miss the target.
Chelsea’s equaliser was as brilliant as it was unexpected, Hazard dancing past Capoue before finishing perfectly past Watford goalkeeper Orestis Karnezis from 25 yards.
Watford responded well and were back in front two minutes later as Janmaat collected the ball on the right before jinking into the box, exchanging passes with Pereyra and keeping his cool to finish past Courtois.
With Chelsea committing bodies forward, Deulofeu capitalised to lead a counter-attack which he started and finished with a well-taken strike, with Pereyra adding insult to injury with a fourth in added time, as Watford won in the league for the first time since St Stephen’s Day.
“It was an unforgettable night,” Watford boss Javi Gracia said.
It was certainly that.
Karnezis, Mariappa, Prodl, Holebas, Janmaat, Capoue, Doucoure, Zeegelaar, Deulofeu (Carrillo 89), Richarlison (Pereyra 65), Deeney (Gray 90).
Courtois, Azpilicueta, Luiz, Cahill, Moses, Kante, Bakayoko, Zappacosta, Willian (Fabregas 34), Pedro (Giroud 64), Hazard.