Raul Jimenez’s deflected strike clinched Wolves a 1-0 win at Leeds and catapulted them up to sixth place in the Premier League table.
Wolves had seen an earlier effort from Romain Saiss ruled out by the video assistant referee for offside.
But Nuno Espirito Santo’s side, rewarded for an improved second-half display, were fortunate to leave Elland Road with all three points having been outplayed in the first period.
Rodrigo headed over and Costa dragged his effort wide after more slick build-up down the right, with Wolves pinned in their own half.
Twice in quick succession from Phillips’ corners, Rodrigo’s thumping drives were blocked as Leeds chased the opening goal they deserved.
Wolves served warning of their threat on the break in time added on at the end of the first half when a fierce Daniel Podence shot was well saved by Meslier.
The visitors enjoyed their best spell at the start of the second period and were denied the opening goal by the video assistant referee.
Saiss thought he had given his side a 54th-minute lead with a superb finish from the edge of the area, but VAR ruled Podence was in an offside position.
Meslier produced a flying save to turn away Podence’s effort shortly afterwards and Leeds all of a sudden had a different fight on their hands.
Wolves added more bite to every challenge and were rewarded for their extra aggression when Jimenez gave them the lead in the 70th minute.
He was allowed too much time to cut inside from the right and after switching onto his right foot, his shot deflected off Phillips’ head, wrong-footing Meslier and into the opposite corner.