Frank Lampard had an early chance to try to get a goal back for the home side as he curled a free kick in towards Branislav Ivanovic, but his delivery did not fall kindly for the defender.
Chelsea continued to push for an early goal, with Oscar crossing the ball in for Samuel Eto'o, but his finish was deflected behind for a corner.
Salvatore Sirigu had to remain sharp as he was forced to make a save with just under half an hour gone as David Luiz tried to force the ball in from long range, shortly after turning away another Lampard free kick.
However, the hosts were able to take the lead just a couple of minutes later when Schurrle, who replaced the injured Eden Hazard early on, collected a flick-on from Luiz before coolly slotting it in.
Gary Cahill had the opportunity to add another shortly before the break as he tried to head in from a Lampard free kick, but his finish went well wide.