Sturridge scores again in Bolton win
The pacy target-man, signed from Chelsea last month, latched on to a knockdown from Lee Chung-Yong to volley powerfully home midway through the second half and maintain his impressive start with his new team.
Defender Gary Cahill opened the scoring early in the match when he found space in the area to head a Stuart Holden free kick into the back of the net with the help of a deflection off Johnny Heitinga.
In driving rain and difficult playing conditions, the game proved to be a damp squib with little goalmouth action.
Everton's best chance came in the first half when Australian Tim Cahill volleyed into the ground and wide from close range.
The hosts thought they had added a third when Holden smashed the ball into the roof of the net in the dying minutes but the linesman ruled that it had gone out of play in the buildup.
Bolton remained in eighth place in the standings on 36 points while Everton are struggling in 13th on 30, just three points clear of the relegation zone.