This was very much a heavyweight contest in terms of physical strength and the visitors were more than willing to slug it out in a toe to toe battle.
And Bolton created the first chance in the 11th minute when Johan Elmander slid in to meet Matt Taylor's cross and force an acrobatic stop from Thomas Sorensen.
But it was a touch of finesse from Glenn Whelan and a square Wanderers defence which led to Stoke taking the lead three minutes later.
Whelan's slide-rule pass was all it took to send Beattie galloping clear and he gave the onrushing Jussi Jaaskelainen no chance with a well-placed shot.
Bolton responded with a typically powerful shot by Taylor which Sorensen was very pleased to clutch to his chest.
And then Stoke hit back in kind with the long throws of Rory Delap - back in the team after a three-match ban - and successive corners by Liam Lawrence applying strong pressure.
Abdoulaye Faye headed over from a Lawrence free-kick as City pressed for a second before half-time in what continued to be a bruising encounter.
But with the snow now driving down, Taylor's 25-yard effort forced Sorensen into another diving stop at the end of the opening 45 minutes.
Bolton also started the second half with attacking intent and Tony Pulis brought on Fuller for the out-of-sorts Mamady Sidibe in the 56th minute.
Fuller was soon swapping passes with Andy Wilkinson before the full-back's 20-yard free-kick was deflected wide for a corner.
But the visitors continued to hold the upper hand until Fuller put Stoke in the comfort zone 17 minutes from time.
The Bolton defence failed to deal with Delap's umpteenth long throw of the night and after Jaaskelainen had parried Whelan's shot, Fuller cracked the rebound into the roof of the net.
Substitute Ibrahima Sonko almost added a third when his 80th minute header crashed against the bar following a Lawrence corner.
But that would have been tough on Bolton who kept going until the end as Sorensen made another fine save to keep out a 20-yard volley from Elmander.