Glenn Whelan, running on to Jon Walter's set-up after Schwarzer had again flapped at an Etherington cross, shot over at the start of the second half, but the Australian goalkeeper was at his best in touching Huth's header over just after the hour mark.
Having offered so little going forward, Fulham then put together a glorious sequence of passes in which both Ashkan Dejagah and Damien Duff were prominent before Dimitar Berbatov fired in a rising angled drive which Stoke goalkeeper Asmir Begovic had to dive to his right to save.
Having finally begun to threaten, Fulham continued to attack, but it was Stoke who had the ball in the back of the net again only for striker Kenwyne Jones's late effort to be ruled out for offside.
"We've just asked Charlie to get closer to 'Crouchie'," said Stoke manager Tony Pulis. "We're pretty structured, organised and disciplined, we need him up around Peter, and if he does that, he'll get opportunities to score."