On-loan Chelsea striker Sturridge opened the scoring in the 14th minute with a superb solo effort.
Lee Chung-yong then headed a second five minutes later when he got on the end of a cross from Martin Petrov.
The home side sealed the points after 51 minutes when Sturridge drifted in from the left and got the better of Scott Parker on the edge of the area before steering a shot beyond Rob Green.
