Stoke gained some welcome relief from their Europa League hangovers, with Tony Pulis' side recording a victory after a European outing for only the second time this season.
Defender Huth's first goal of the campaign early on proved to be enough as Everton missed the chance to pick up a third successive league win for the first time in 22 months.
They were not without their chances, however, and should have had a penalty just before half-time and could easily have had another after the break.
Ultimately, with teenager Apostolos Vellios making only his second start for the club up front in place of the absent Louis Saha, they did not pose enough of a threat in the opposition penalty area despite dominating the second half.
Stoke, who due to their European commitments had already played nine matches more than their hosts, improved on their woeful away record this season - ending a run of four successive defeats on the road.
There was a low-key start to the game after tributes were paid to former Toffees captain and Wales manager Gary Speed, who died last weekend.
Both teams walked out to the Welsh national anthem as opposed to the familiar Z Cars theme tune.
Speed's father Roger was among a number of his son's former team-mates invited on to the pitch to join in a minute's applause before kick-off, while mascots wearing the kits of Wales and all the clubs represented by the midfielder joined the group around the centre-circle.
Stoke defender Jonathan Woodgate, a former team-mate at Newcastle shared an embrace with Speed senior, before taking up an unfamiliar right-back position.
There was little in the early exchanges with Diniyar Bilyaletdinov bundling a shot so wide it failed to go out after a flick on by Apostolos Vellios, making only his second Everton start.
The Russian's next intervention, however, led to the opening goal.
His weak header from Matt Etherington's 15th-minute corner dropped to Dean Whitehead on the edge of the penalty area and he drilled in a shot which Huth turned past Tim Howard from close range.
Prior to kick-off, they had taken just four points and scored just three goals in six matches.
But it was no surprise the winner should come from a corner, as nine of their 14 league goals this season have been from set-pieces.
Bilyaletdinov, having been kept out of the side for most of the campaign, seemed to be involved everywhere with one hanging cross being clawed out under his own crossbar by goalkeeper Thomas Sorensen.
It was Stoke, though, who seemed to be posing the greater goal threat and when Glenn Whelan's left-wing corner was flicked on both Ryan Shotton and Ryan Shawcross, with the latter also seeing a header tipped over by Howard.
Everton midfielder Marouane Fellaini was convinced he should have had a penalty on the stroke of half-time when he nodded Bilyaletdinov's corner wide.
The Belgium international claimed he was being held by Shawcross and television replays suggested he was right.
Everton had another penalty shout in the 67th minute when Huth opted to leave Leighton Baines' chipped pass and Tim Cahill nipped in front of Sorensen.
The two collided, with the Denmark goalkeeper seemingly failing to connect with the ball, but referee Mason - possibly influenced by an injury to Sorensen - awarded only a corner.
Despite the chorus of disapproval from the majority of Goodison Park, the injury appeared to be a genuine one as, only a couple of minutes later, the dazed goalkeeper left the field on a stretcher.
His replacement Asmir Begovic, deposed as first choice this season, was not exactly tested in the remainder of the game.
The closest Everton came to threatening was in the 86th minute but even then John Heitinga failed to get his head on Baines' cross from six yards out.
Seven minutes of added time failed to provide an equaliser and Everton's mini-revival of back-to-back wins came to a shuddering halt.