This win, following last weekend's 1-0 success at Watford, moved the Potters up two spots to ninth.
Last year's Championship champions Burnley, without a win away from home, slip one place to 14th.
The visitors started brightly but a classy goal from Walters, his first since mid-March, set Stoke on their way in the 20th minute.
The Republic of Ireland forward connected with Mame Biram Diouf's low cross to arc the ball expertly past Burnley goalkeeper Paul Robinson.
This was the silver-haired 33-year-old's 40th goal for Stoke.
The Potters were causing Burnley all kinds of trouble, and the home side deservedly extended their lead 10 minutes from the break.
Their second goal came from an unlikely source, from centre-back Muniesa who has had precious little playing time this term.
But the Spaniard, who arrived at the Britannia Stadium on a free transfer from Barcelona in 2013, registered his first ever goal in the Premier League with a left footed volley into the far corner after an assist from the agile Marko Arnautovic.
Walters looked set for his second as half-time approached but was denied a chance to shoot by stout defending from Ben Mee.
Hughes introduced Joe Allen, back after a one match ban, in place of Xherdan Shaqiri on the hour and shortly after the Wales midfielder had a shot saved by Robinson.
Hughes was then forced into making an unscripted substitution when the lively Arnautovic had to come off after a clash with Jon Flanagan, with Peter Crouch taking his place.
Hard though Burnley tried they were unable to make any inroads and in the dying minutes only good work from Robinson denied a shot from Allen.