Gretar Steinsson, Kevin Davies and Johan Elmander all found the net for the hosts in the first 45 minutes to leave City licking their wounds.
Stoke, who last played a game in England's top tier back in the 1984/5 season, were completely overrun by a Wanderers side who are now unbeaten in six games if you take the end of last season into consideration.
City did however grab one back when substitute Ricardo Fuller headed home deep into second-half injury time.
Right back Steinsson, the Icelandic £3.5million capture from AZ Alkmaar back in January, opened the scoring on 34 minutes when he cushioned Kevin Nolan's neat ball before unleashing a swerving cross that evaded debutant Thomas Sorensen and ended up in the net.
It was the 26 year-old's first goal for the club and highlighted his growing importance to Gary Megson's side.
Targetman Davies doubled the lead seven minutes later when he neatly headed home a deep Gary Cahill cross.
And then Elmander, the club's record £11million summer signing from Toulouse, nodded in the third from Joey O'Brien's accurate free-kick in first-half injury time.
Midfielder Seyi Olofinjana saw a header flash over the bar midway through a quiet second half.
Bolton captain Nolan saw a weak shot cleared off the line, while wing-back Matt Taylor also had an ambitious flicked volley well saved by former Aston Villa keeper Sorensen.
Wanderers actually took their foot off the gas in the second period and boss Megson will not be happy at the lack of a clean sheet.
However, the immediate three points settled any lingering fears among the home fans that they will struggle at the wrong end of the table for a second successive season.