Bilic's side celebrated the first Premier League fixture in their new home with a 1-0 victory over 10-man Bournemouth yesterday thanks to Michail Antonio's 85th minute header.
Impressive Turkey winger Tore baffled Adam Smith with some nifty footwork before lofting a cross to the far post, where Antonio rose highest to head home from close-range.
West Ham's cause was helped by Bournemouth's Harry Arter, who was shown the stadium's first red card with 12 minutes left.
West Ham United manager Slaven Bilic gestures during the club's Premier League match against West Bromwich Albion in Upton Park, London November 29, 2015.
West Ham's Arthur Masuaku then tried to influence proceedings in the east London sunshine but his shot on 22 minutes, after a poor Tore free-kick, was well saved by Artur Boruc.
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Michail Antonio scored the first ever Premier League goal at West Ham's new home.
Yet Bournemouth still could have spoiled the party but for Adrian's save from King and Winston Reid's courageous block to deny Simon Francis on the follow-up. Unfortunately the mistake for us was going down to ten men. It was hard, but we knew it would be.
Striker Jonathan Calleri, who joined on loan from Uruguayan Segunda Division outfit Deportivo Maldonado last week, spurned a glorious chance to extend the lead in second-half injury time after bursting through on goal. We have to be better on that.
"That's the one that has to disappoint, the first booking", said Bournemouth manager Eddie Howe, whose side are bottom after two games. Hopefully he'll be back in December, so we are going to try to get one if possible. But I will talk with the directors on Monday morning about getting one, and if we do it will be a good one, but if not we will survive anyway.
"I had seen it when I came to sign for the Club at the Juventus game." said Masuaku after the win over Bournemouth.