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Britos stabbed home at the death after Liverpool had come from 1-0 and 2-1 down to lead 3-2 thanks to a three-minute blitz in the second half, when new signing Mohamed Salah made an impact.
Former Chelsea winger Salah, who joined Liverpool from AS Roma during the close season, won a penalty converted by Roberto Firmino in the 54th minute and then bundled in the Brazilian's lofted pass from close range.
Liverpool's Sadio Mane scored a classy equaliser to cancel out striker Stefano Okaka's early header for Watford, but midfielder Abdoulaye Doucoure put the hosts 2-1 up in the first half after sloppy defending by Liverpool.
Rooney scores winner on Everton return
Wayne Rooney marked his Premier League return in Everton colours with the winning goal in a 1-0 victory over Stoke City at Goodison Park.
Rooney, who was full of invention and energy throughout, rose well to meet a fine Dominic Calvert-Lewin cross with a looping header into the far corner on the stroke of halftime.
The former England captain rejoined his boyhood club last month after 13 years with Manchester United.
Everton's new goalkeeper, Jordan Pickford, pulled off a superb save in injury time to deny Xherdan Shaqiri an equaliser from a long-range drive.
Aguero helps City to win
A clinical Sergio Aguero strike and an own goal by Lewis Dunk condemned Brighton to a losing return to England's top flight as they lost 2-0 to Manchester City at the Falmer Stadium.
Back in England's top division for the first time in 34 years, the Seagulls spent most of the game on the back foot, content to concede possession and setting up a compact defensive unit deep in their own half.
City's Gabriel Jesus had two goals ruled out - for handball and offside - and Pep Guardiola's team struggled to break Brighton down until Aguero fired home a pass from David Silva to open the scoring in the 70th minute.
Five minutes later, Brighton defender Dunk slammed a header into his own net as he tried to clear a cross under pressure from Gabriel Jesus, with the home side lacking the firepower to mount a comeback.