Huth opened the scoring with a powerful 51st-minute header from a Matthew Etherington corner and Wilson wrapped up the points by knocking home the simplest of chances in injury time to snap their run of three Premier League games without a win.
And Kean will know it could have been much worse for his side with Etherington missing an early sitter and Kenwyne Jones forcing a wonder save out of Paul Robinson late on.
For all the new Rovers' owners heady predictions, the defeat made it clear that Kean's more immediate concern is sorting out the future of unsettled stars like defender Christopher Samba.
Rovers looked susceptible to set-pieces all afternoon and Huth grabbed the lead by darting ahead of the static Mame Biram Diouf to power home Etherington's corner.
It was rich reward for Tony Pulis' men who looked the better side throughout and shaded a dismal first period made memorable only by Etherington's astonishing 14th-minute miss.
Ryan Shawcross rose highest in the box to nod on a Rory Delap long throw and find Etherington, only for the midfielder to tap the ball across the face of goal from point-blank range.
Brett Emerton poked a half-chance wide for Rovers after 20 minutes from a cross from the left by Martin Olsson, who was by far the home side's best player on the flank.
With the bitingly cold weather not helping, both sides struggled to fashion clear-cut openings but the visitors created a couple of opportunities just past the half-hour mark.
First the impressive Jon Walters, back from a bout of 'flu, came close in a scramble before Huth's header in the box from a Jermaine Pennant free-kick was booted clear by Gael Givet.
A poor first half ended with a spate of bookings with Stoke's Andy Wilkinson and Shawcross, and Rovers' Nikola Kalinic all finding themselves yellow-carded for poor challenges.
Huth broke the deadlock with the goal that was impressive for its simplicity, charging in front of the static Diouf to angle Etherington's corner past Robinson.
Rovers belatedly stirred, the busy Givet close to connecting to a Morten Gamst Pedersen free-kick then Diouf heading into Asmir Begovic's hands from an Emerton cross.
But the visitors came close to adding a second in the 64th minute when Delap wriggled clear on the right and sent in a superb cross to Dean Whitehead, whose header was caught by Robinson.
Three minutes later Stoke countered swiftly through Pennant and his cross from the left found Jones, whose close-range header was brilliantly tipped over the crossbar by Robinson.
Jones wriggled through a static Rovers rearguard before being pushed into touch by Robinson as the home fans began to show their frustration with their side's display.
Begovic punched clear under pressure from a Pedersen corner and with time running out Emerton thumped in a long-range effort which was deflected out for another set-piece.
From it, youngster Grant Hanley saw his firm header well saved by the increasingly busy Begovic, then Diouf fumbled a shooting chance in the box after being set up by Michel Salgado.
To compound the agony for Kean, Stoke wrapped up the win in injury time when substitute Ricardo Fuller crossed for Wilson to knock home the simplest of chances.