Goals from Cheikhou Kouyate and Edimilson Fernandes earned West Ham a third consecutive win to put them in the quarter-finals of the competition while Gary Cahill's stoppage time consolation went almost unnoticed as trouble brewed.
Special security measures had been put in place for the most volatile match yet staged at West Ham's new stadium, including an alcohol ban and a reduction in tickets on sale.
For the most part the 45,000 crowd were boisterous but orderly until, with victory virtually secured for West Ham, rival fans began surging towards each other behind the goal guarded by home keeper Darren Randolph.
Stewards had their hands full trying to keep hundreds of fans apart and several plastic seats were ripped out and thrown from the home fans towards the Chelsea section.
Police in riot gear finally arrived to quell the trouble before it got out of control although further disturbances were reported outside the ground.
In a statement, the club said: "West Ham unreservedly condemn the behaviour of individuals involved in incidents during this evening's fixture with Chelsea.
"Once identified, those found to have acted improperly will be banned from attending any West Ham United fixtures for life."
West Ham manager Slaven Bilic became agitated when the post-match news conference quickly turned to events off the pitch.
"Ask me one question about the game, 2-1, it was a London derby," Bilic told reporters. "It's a little unfair towards the game and the players who played in the game.
"Of course I saw it (the trouble). But I was concentrating on the game and telling (Aaron) Cresswell not to watch it, but watch the game. Whatever happened we are totally against it as a club. For those kind of things to happen it's unacceptable."
West Ham's move from their historic Upton Park ground to the former London 2012 Olympic Stadium has been far from smooth.
Home Premier League matches against Watford, Middlesbrough and Bournemouth were all marred by crowd disturbances inside and outside the ground, some of it between West Ham's own fans.
The club said 23 fans have already been banned this season.
"I don't really like to see these situations. It's important to always see the right atmosphere and in England this aspect is fantastic," Chelsea manager Antonio Conte said.
A Chelsea spokesman added later: "The club is extremely disappointed to see disturbances at the end of tonight's game and we condemn such behaviour.
"I'm unable to comment further until tonight's incidents have been investigated properly."
The trouble overshadowed a compelling tie in which Conte's side come back to earth after Sunday's 4-0 hammering of United.
Conte made seven changes from the weekend but said he was satisfied with the display.
"Today we were a bit unlucky in this aspect," the Italian said. "I think the young players played a good game with the right intensity and concentration.
"Tonight I found a lot of positive things."
(Reporting by Martyn Herman, editing by Pritha Sarkar)
