Sturridge extended Bolton's lead after England defender Gary Cahill opened the scoring with his first goal of the season.
Bolton got off to a perfect start with Cahill opening the scoring in the 10th minute following Stuart Holden's free-kick on the left flank.
He peeled away from his marker and saw his header come off Everton defender John Heitinga and wrong-foot Tim Howard.
Bolton went 2-0 ahead in the 67th minute with Sturridge's third goal in three matches since arriving on loan from Chelsea.
The striker smashed the ball into the corner from an acute angle following a flick-on from Chung-Yong Lee.
Source: PA
Source: PA