Burnley gave home debuts to home keeper Mike Pollitt, midfielder Eric Djemba-Djemba and striker Ade Akinbiyi.
Playing their first home game for a month, the Clarets began brightly with Gifton Noel-Williams testing Stoke keeper Steve Simonsen with a left-foot half-volley.
At the other end, Stoke forced two early corners, the second of which led to Mamady Sidibe placing a free header straight at Pollitt.
Stoke took the lead in the 24th minute when Fuller held off a challenge from Michael Duff to get to the byline and pull the ball back for Sidibe to score from close range - his sixth goal of the season.
Fuller should have increased the lead moments later, once again beating Duff but placing his shot too close to Pollitt.
The home side almost forced an equaliser when Noel-Williams had a shot on the turn cleared off the line by right-back Andy Wilkinson.
Sidibe then created an opportunity with a clever improvised pass which Darel Russell failed to convert from the edge of the box.
With half-time approaching Akinbiyi forced a save from Simonsen after a good cross by Jon Harley.
At the interval Burnley boss Steve Cotterill replaced midfielder Chris McCann with Northern Ireland teenage striker Kyle Lafferty.
In addition, defenders Duff and Frank Sinclair swapped positions in a bid to create a stronger defensive unit. However, the Burnley defence continued to look uneasy as further hesitation resulted in Sidibe testing Pollitt.
Cotterill then handed a debut to recent signing Joey Gudjonsson who replaced Djemba-Djemba as Burnley continued to struggle to make any inroads against the well-marshalled Stoke defence.
The final throw of the dice from Cotterill saw Garreth O'Connor replace winger Wade Elliott.
A mistake by former Potter James O'Connor gave the visitors the chance to finish off the game but Dominic Matteo's shot was well-saved by Pollitt.
Stoke had strong claims for a penalty near the end as Fuller got to the byline and appeared to be brought down by Duff but referee Pike was unimpressed.
In stoppage-time the home side almost scrambled an undeserved equaliser when Noel-Williams' header was parried by Simonsen who did well to gather the rebound off the toes of Akinbiyi.