The impressive Swedish international struck Bolton's third goal just before half-time to make it a perfect start for Gary Megson's side.
Stoke were marginally better in a dreadful opening half hour before Gretar Steinsson netted the first of three goals in 15 minutes.
The Icelandic full-back's first goal for the club was a spectacular one, albeit an intended cross to the far post.
Kevin Davies, who didnt register his first goal last season until December 9, held off the challenge of two defenders to glance in Wanderers second.
And new dad Elmander rounded off a memorable few weeks by heading home Joey O'Brien's free kick.
Former Preston striker Ricardo Fuller headed Stoke’s consolation in the last seconds of stoppage time.
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Nice start but anything less than 3 points against a newly promoted team would have been worrying. Given the fixtures for August the Whites should be in the top 6 in 4 weeks time and should take away any anxiety, at least untill Christmas.