Leeds pushed hard for an equaliser but Mateusz Klich hit a post and Patrick Bamford had a goal ruled out for offside.
Wolves moved above Leeds into 11th place after extending their recent upturn in form, while Leeds have lost three of their last four league games.
The tone for an entertaining encounter was set when Raphinha slipped in Klich and the midfielder’s low effort ricocheted off the near post.
Pascal Struijk’s follow-up was saved by Rui Patricio and Raphinha eventually fired wide.
Wolves responded and Meslier had to parry Nelson Semedo’s angled effort.
Meslier needed to be alert to deny Semedo again just before the break.
Wolves forward Pedro Neto seized on Jack Harrison’s loose pass to fire over early in the second half.
Raphinha’s whipped delivery was met by Liam Cooper and his header was parried by Patricio, with Bamford’s follow up smuggled away.
That save proved crucial as Wolves instantly regrouped to snatch their fortuitous 64th minute winner.
Traore collected the ball on the left and shrug off Luke Ayling as he surged towards the Leeds area.
The winger’s 25-yard drive rattled the underside of the bar and the ball bounced out, hit Meslier on the back and rolled across the line.
Patricio saved from Cooper as Leeds sought a quick response and Bamford had an emphatic finish ruled out for offside.
Yet a leveller never came thanks to two smart stoppage-time saves from Patricio, who denied Helder Costa and turned away Raphinha’s header.