Antonio Conte's disjointed side struggled from the early stages when captain Gary Cahill was dismissed for a lunging tackle and they found themselves three-nil down at halftime to a team who gained only seven points away from home all last season.
Wales international Sam Vokes scored two of the goals and Stephen Ward the other.
New signing Alvaro Morata from Real Madrid came on to pull one back midway through the second half and then provided an assist for David Luiz, but in-between midfielder Cesc Fabregas was also sent off for a second yellow card.
It was a dispiriting afternoon for Conte, who won the title in his first season at the club but has complained that Chelsea have not signed enough new players while allowing several to leave.
Liverpool manager Juergen Klopp protested that Watford's stoppage-time equaliser by Manuel Britos in an entertaining 3-3 draw should have been disallowed for offside.
Britos was standing almost on the line before nudging in the loose ball after Simon Mignolet pushed it onto the bar.
"We were unlucky in the end," Klopp said. "The equaliser was offside. It’s obvious because the linesman is on the line. He needs to see it.
"We would have had defensive areas we need to work on if we’d won 3-2. We were the better team, we should have won."
After the opening game of the season on Friday produced seven goals and a late winner for Arsenal, who beat Leicester City 4-3, the two teams at Vicarage Road served up more of the same entertainment for a worldwide television audience -- including some poor defending.
The home side, under new manager Marco Silva, led twice through Stefano Okaka and Abdoulaye Doucoure but Sadio Mane and Roberto Firmino, with a penalty, both equalised.
Debutant Mohamed Salah seemed to have won the points for the visitors before Britos's dramatic late intervention.
Promoted Huddersfield Town, playing in the top flight for the first time since 1972 and widely tipped for relegation, cruised to a 3-0 win away to Crystal Palace.
Record signing Steve Mounie, the Benin striker from Montpellier who cost 13 million euros ($15.36 million), scored once in each half after Palace's Joel Ward put through his own goal.
Wayne Rooney scored on his return to Everton from Manchester United to give the Merseysiders a 1-0 victory at home to Stoke City. It was his 199th Premier League goal and first for Everton since 2004.
Egyptian defender Ahmed Hegazi, on loan to West Bromwich Albion from Al Ahly, scored on his debut in the 1-0 win at home to Bournemouth.
There were no goals on the south coast between Southampton and Swansea City. That meant the Saints have not scored at home in their last six games.
Promoted Brighton were playing at home to Manchester City in the late game on Saturday.
($1 = 0.7686 pounds)
($1 = 0.8463 euros)
(Editing by Neville Dalton)
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