Sturridge is looking like one of the signings of the January transfer window after grabbing his third goal in three games for the Trotters.
On loan from Chelsea, the England Under-21 striker put the match out of Everton's reach after Gary Cahill opened the scoring with his first goal of the season.
It was just the result the club were looking for after losing five out of their previous seven league games.
They 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-footed Tim Howard.
Everton responded and should have equalised in 17th minute when Tim Cahill was left unmarked at the back post but volleyed wide following a cross from Leighton Baines.
Bolton were forced to make a switch in the 27th minute with defender Zat Knight unable to continue. He fell awkwardly after tangling with Victor Anichebe and was replaced by David Wheater.
The home side kept up the pressure and won a free-kick 20 yards out after Heitinga was adjudged to have tripped Sturridge as he tried to race forward.
Matt Taylor stepped up but only succeeded in drilling his effort into the arms of Howard.
Everton again found themselves on the back foot in the 39th minute when Holden delivered a free-kick to the back post. Howard, however, punched clear with Wheater waiting for any slip-ups.
Play switched down the other end and Cahill tested Bolton goalkeeper Jussi Jaaskelainen from the edge of the area.
The home side were looking the brighter of the two teams at this stage and Taylor attempted to pick out Sturridge in the area a minute before half-time.
However Phil Neville was perfectly positioned and made the interception at the post to concede a corner, much to Everton's relief.
Bolton started the second half on the front foot and won a free-kick in the 51st minute after Sturridge was tripped by Marouane Fellaini.
Taylor stepped up 20 yards out but his effort failed to breach the defensive wall.
Everton suddenly turned up the pace and Anichebe got into a good position in the area in the 56th minute only for Cahill to make a crucial block for Bolton.
Then Fellaini was set up by Seamus Coleman but he sent his effort high and wide of the woodwork.
Bolton manager Owen Coyle decided to freshen things up in the 59th minute by bringing on Lee Chung-yong for Taylor.
This was a good spell by Everton with Cahill beginning to find more room in and around the area. He then sent a snap shot over the bar five minutes later.
However 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 Lee.
Holden found the net for Bolton in the 80th minute after a back heel from Sturridge. However, referee Lee Probert ruled out the American's effort, the lruling that Sturridge had run the ball over the by-line.
Everton responded and substitute Jose Baxter rattled in a shot three minutes later that was parried by Jaaskelainen.
Johan Elmander almost added a third for Bolton two minutes after Kevin Davies' knock-on, only to see his effort go marginally wide of the target.
While Bolton were celebrating, these remain worrying times for Everton after only two wins in the league on the road.