Boro's Cristhian Stuani struck twice in the first half to earn the points, while a Michail Antonio header gave West Ham the spoils against a Bournemouth side reduced to 10 men in the 78th minute when midfielder Harry Arter was sent off.
It was a historic day for West Ham United as they began their Premier League life at their new stadium.
West Ham were victorious yesterday against Bournemouth during their first game at their new stadium, the London Stadium.
The 26-year-old winger rose at the far post to head Gokhan Tore's cross beyond Cherries goalkeeper Artur Boruc with just five minutes left.
The turning point came when Arter, already on a booking, was dismissed in the 77th minute for a second yellow card after hauling down Cheikhou Kouyate on the halfway line.
West Ham United will take on Astra Giurgiu in their Europa League play-off at the London Stadium on Thursday, August 25 with kick-off at 7:45pm BST.
If West Ham are to fulfil Bilic's prediction of an atmospheric first season in the London Stadium, they will need better luck with injuries than they are now experiencing.
"At a time when the club is growing its global portfolio, it is all the more important that we remain true to our rich heritage and so it is particularly pleasing to have joined forces with a prominent local business", said West Ham vice chairman Karren Brady.
"I'm not paid to say I like the new stadium if I don't like it, but I thought the atmosphere was brilliant", Bilic said. 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.
With Dimitri Payet and Andy Carroll - who Bilic confirmed is set to miss several weeks with a knee injury - having joined West Ham's growing injury list, Bilic's side lacked guile in the final third, though Tore did go close with a curling effort that sailed just over. I felt we were pushing to get the victor.
"You're asking me about him, okay". We know the rules, we are well drilled.
Bournemouth manager, Eddie Howe, said: "It was a tight game with little goalmouth action". I think the chairmen are going to be very generous, if we can find a proper one, but a proper one is very hard to find.