The Scotland striker took his tally to four goals in four games to end a five- match run without a win for Mick McCarthy’s side.
Adlene Guedioura was also on target for the home side while Albion’s only reply came from a Peter Odemwingie penalty.
The home side dominated the opening 45 minutes with Stephen Hunt a livewire figure and Fletcher and Stephen Ward a constant threat upfront.
Albion looked to be suffering a hangover after securing their own top-flight future for another season and were pulled apart defensively.
It was a different story in the second period when they created several opportunities.
But Wolves managed to survive to put their destiny back in their own hands with two games remaining.
Wolves started on the offensive and Scott Carson was forced to turn aside a free-kick from Jamie O’Hara.
But from the corner Fletcher put Wolves ahead with his 10th goal of the season – and his third in the last four games.
Hunt’s centre was flicked on by Guedioura inside the six-yard box and Fletcher applied the finishing touch.
Guedioura came close to doubling the lead when his free-kick curled just over the bar.
It came as no surprise when Wolves doubled their lead after 27 minutes with a goal similar in build-up to the opener.
Hunt’s corner was headed back across goal by Fletcher and the unmarked Guedioura volleyed past the exposed Carson from close range.
The visitors were conceding a stream of free-kicks and George Elokobi headed over the bar from an O’Hara ball across the box.
A low cross from Ward just eluded the run of Hunt as West Brom were again carved open at the back.
Fletcher was causing constant problems in the air and he headed just wide from an O’Hara corner.
Peter Odemwingie could have pulled one back in first half injury-time but drilled his shot wide of the far post after skipping past two players.
But Wolves extended their lead two minutes into the second period after a mistake by Abdoulaye Meite.
The Baggies defender looked to have covered a through ball from Kevin Foley.
But he allowed the ball to slip under his foot and left Fletcher with a clear run at goal and he kept his cool before clipping the ball past Carson into the corner of the net.
Hennessey dealt with a shot from Thomas at the second attempt while a deflected attempt from Guedioura flew past the post.
But after 54 minutes Odemwingie gave the Baggies a ray of hope from the penalty spot.
Guedioura brought down Thomas – he was yellow carded for the offence – and Odemwingie planted the spot-kick into the corner of the net.
It was his 15th goal of the campaign and means he has been on target in five successive Premier League games.
Albion still looked suspect in dealing with set-pieces and Shorey cleared a goal-bound flick by Henry from a Hunt corner.
Youssouf Mulumbu was booked for bringing down Guedioura.
Albion were looking more threatening and Hennessey produced a fine save to keep out a volley from Morrison away to his right.
Then Thomas hammered his shot against the crossbar after seizing onto a pass from Tchoyi.
The visitors were in the ascendancy and Tchoyi headed over when well placed from Mulumbu’s cross.
Albion substitute Marc-Antoine Fortune turned past the challenge of Jody Craddock but was slightly off balance when he lofted his shot wide.
Ward could have made it 4-1 but pulled his shot wide with only Carson to beat and the Albion keeper then denied Sylvan Ebanks-Blake.