Chelsea produced a solid second-half performance to claim all three points in the opening game of Champions League Group E.
The Blues lined-up without skipper John Terry and vice-captain Frank Lampard, but were quick out of the blocks and had an early goal disallowed for the unfortunate Fernando Torres.
Both the Spaniard and Daniel Sturridge had further shots blocked by keeper Bernd Leno, but the Bundesliga side were never out of the tie and had their own goal controversially disallowed.
And it was the visitors who had the best chance in the second-half, with former Blues midfielder Michael Ballack breaking into the penalty area but finding the legs of Petr Cech when one-on-one with the keeper.
Soon after the former German international captain's exit, defender David Luiz broke the deadlock for the hosts, with the Brazilian charging forward and striking a beautiful sweeping shot into the far post from Torres' layoff on 67 minutes.
Juan Mata was denied minutes after, but he put the result beyond doubt when Torres beat the last defender and squared for his compatriot to slide the ball home into an empty net.