Two of Chelsea's three Premier League defeats this season were away London derbies -- to Arsenal and Tottenham -- and West Ham beat the Blues in the EFL Cup in a match marred by crowd trouble at the London Stadium.

Those scenes -- of violence and a Chelsea defeat -- were not repeated here, although one fan hurdled the advertising hoardings to remonstrate with celebrating Chelsea players after Hazard's goal before he was wrestled away.

Chelsea head coach Antonio Conte may be taking nothing for granted in the title race, but his side are showing little sign of slipping up.

Tottenham are the Blues' nearest rivals with 11 games to go, but third-placed Manchester City could move eight points behind by winning their game in-hand.

West Ham's direct tactics were predictable, but Chelsea withstood the bombardment until Manuel Lanzini's stoppage-time strike, which proved mere consolation.

Slaven Bilic would have anticipated the visitors playing on the counter-attack, but his side could not stop Chelsea going in front once the excellent N'Golo Kante had intercepted a Robert Snodgrass pass intended for Sofiane Feghouli.

Ten seconds later the ball was in the Hammers' net as Hazard struck his 10th of the campaign. While, Costa bundled in his 17th and now has 49 Premier League goals.

Next the Blues play Jose Mourinho's Manchester United, who they beat 4-0 in the league, in the FA Cup quarterfinals.

Conte, Mourinho's permanent successor, on Friday spoke of Hazard receiving a kick in training and he was fouled twice in the opening four minutes.

Victor Moses beat Andy Carroll in the air to head clear a Feghouli cross from the right. The Hammers striker suffered a cut to his nose which needed running repairs.

Swarming black shirts were wary of the aerial threat of Carroll, with Snodgrass and Feghouli providing the artillery.

Chelsea's defence was holding up well; far better than Gary Cahill's shirt which had to be replaced when it ripped in half.

And the opening goal came after 25 minutes, from a promising position for West Ham.

Lanzini struck a free-kick into the wall and Kante nipped in before bursting forward.

He fed Hazard, who found Pedro and then continued his run. Hazard stayed onside and kept his balance as Darren Randolph lost his to do the rest.

The Hammers defence had been breached. There was immediately a security concern as a man evaded the stewards to approach the celebrating Chelsea players. He was swiftly shackled by three stewards and taken away.

Chelsea's confidence grew. Lanzini fired over after driving through the centre and exchanging passes with Mark Noble, but seconds later it should have been 2-0.

Costa was slightly in front of Hazard's cross and failed to get a clean connection. The ball ran for Moses, whose shot was blocked by Aaron Cresswell, then Randolph denied Pedro.

Chelsea had their second five minutes after the resumption.

A Cesc Fabregas corner evaded West Ham's near-post defenders and the ball bounced in off Costa's thigh.

Marcos Alonso lifted the ball narrowly wide moments later after beating three would-be tacklers.

Next Carroll shot over for West Ham, Thibaut Courtois repelled Snodgrass' cross and then Jose Fonte headed wide.

Nemanja Matic was sent on for Pedro to protect Chelsea's lead as Conte switched to a 3-5-2 formation and the Blues soon almost had a third before Randolph saved smartly after Costa turned Kouyate.

The leaders faced an anxious conclusion as Lanzini struck after substitute Andre Ayew ran at David Luiz - but West Ham ran out of time to find an equaliser.