The pair struck in quick succession just before half-time in a fierce Premier League derby, Jones brilliantly flicking and volleying in a free-kick and Fletcher turning in from close range.
Stoke replied with a powerful Abdoulaye Faye header but missed record signing Kenwyne Jones, who hit the bar early on but limped off after 13 minutes.
The Potters made life tough for Wolves in a full-blooded second half but the hosts created, and squandered, the better chances.
In the end victory was just reward for manager Mick McCarthy, whose side attacked with verve despite missing last season's top scorer Kevin Doyle through injury.
Kenwyne Jones went straight into the Stoke side despite the doubts expressed by manager Tony Pulis about his match-fitness after his £8million move from Sunderland this week.
Faye and Glenn Whelan also started after overcoming injury while Thomas Sorensen retained his place in goal despite pressure from Asmir Begovic.
Kenwyne Jones wasted no time in making his presence felt as broke down the right and burst into the area to fire a shot against the crossbar with just three minutes gone.
In a ferocious opening that matched the intense atmosphere, Rory Delap needed to leave the field to have his head bandaged.
David Jones put the ball in the net for Wolves before Delap returned to the field but the strike was ruled out for a foul on Sorensen.
Confusingly, Delap came back wearing a different number but, more worryingly, Kenwyne Jones took his place on the sidelines after falling awkwardly in a challenge from Jody Craddock.
He received treatment but was unable to return and, just 14 minutes into his second debut for Stoke, was replaced by Mamady Sidibe.
Wolves began to take control and created a good chance when another impressive debutant Jelle van Damme, operating as midfielder, crossed into the box but former Burnley star Fletcher fired over.
The hosts appealed for a penalty when the ball took an awkward bounce and caught Faye at the top of the arm but referee Lee Probert deemed it accidental.
Wolves continued to bombard the box and they again called for a penalty when Fletcher had a shot blocked.
Probert waved play on and, amid panic in the Stoke defence, Sylvan Ebanks-Blake shot at Sorensen, Fletcher had another effort blocked at Jones scuffed a shot.
They finally claimed a deserved lead on 37 minutes after Kevin Foley was fouled on the edge of the area by Dean Whitehead.
Karl Henry rolled the ball to Jones and he brilliantly flicked it up to volley into the top corner.
Wolves followed up with a second just two minutes later as Christophe Berra's cross took a deflection and looped over Sorensen for Fletcher to bundle in for a debut goal at the far post.
Matt Jarvis went close to a third in first-half injury time but his shot was deflected for a corner.
Fletcher had another attempt early in the second half but it flew well over and he was replaced by Andy Keogh moments later.
Pulis also decided to make a change and took off Kenwyne Jones' ineffective replacement Sidibe to send on Tuncay.
The Potters hauled themselves back into the game after 55 minutes when Matthew Etherington, one of their more impressive players, picked out Faye from a corner.
The Senegal defender made no mistake as he powered a header past Marcus Hahnemann.
Ricardo Fuller then got a header to a typically long Delap throw but Hahnemann dealt with it comfortably.
Wolves responded with another good spell of their own and Jarvis narrowly missed with a powerful shot from outside the area.
Stoke were fortunate to survive after David Jones forced Sorensen to palm onto the bar with a flying volley.
Wolves felt Danny Higginbotham then handled the rebound but the ball worked its way out to Stephen Ward, who somehow sidefooted wide.
Keogh strangely became the second substitute to be substituted when he was replaced by Greg Halford in the closing moments.
David Jones had another chance to make victory certain with a shot that dipped wide in the last minute.
Delap wound up for one last throw in a bid to snatch a draw in injury time but the ball slipped from his grasp and a foul throw was awarded.