Ivan Toney missed three decent chances in the opening period while Josh Dasilva also curled a shot narrowly wide for Brentford.
Wolves' Joao Moutinho volleyed just off target from a corner while Costa got on the end of a cross but his header flew over.
With the forwards all misfiring it was Mee who opened the scoring from a short corner, when he acrobatically turned in a cross from Bryan Mbeumo.It was a spectacular goal, but it was canceled out just 110 seconds later.
Nelson Semedo collected the ball from Adama Traore and squared to Neves, who crashed a superb first-time effort past David Raya from the edge of the box.
Costa had the best chances to win it for the visitors when he twice wriggled his way into shooting positions but Raya made two fine saves.