Goals from Brazilian duo Alex Teixeira and Fernandinho sealed the result for Shakhtar, who have not lost at the Donbass Arena since November last year.

Oscar netted a late consolation for the lacklustre visitors, whose path to the knockout phase looks far more perilous after failing a stern test away from home.

The Ukrainian side took the lead three minutes in when Luiz Adriano's attempted shot struck Chelsea captain John Terry and broke for Teixeira, who calmly slotted the ball beyond a helpless Petr Cech.

Chelsea tried to rally following the interval but fell into further trouble when Eden Hazard gave the ball away cheaply, allowing Adriano to find Fernandinho, who struck past Cech in the 52nd minute.

Roberto Di Matteo's men gave themselves faint hope of a comeback on 88 minutes when Branislav Ivanovic crossed low for Oscar to tap home, but the goal arrived too late, as Shakhtar ran out worthy winners.

In the other Group E fixture, Danish champions Nordsjaelland claimed their first ever Champions League point with a 1-1 draw at home to Juventus.

Mikkel Beckmann put Nordsjaelland in front after 50 minutes with a brilliant free-kick before the Italian champions equalised with nine minutes to go courtesy of Mirko Vucinic's sharp volley.

Shakhtar are on top of the group with seven points, followed by Chelsea on four and Juventus on three after three matches played.