Wolves, missing talisman Raul Jimenez through injury, could not convert their chances in the first half but had a solid start after the break as Moutinho struck in the 48th minute.
The 35-year-old played a clever one-two with Nelson Semedo on the edge of the box before smashing the ball into the bottom corner with the outside of his foot.
Brentford responded in the 71st minute with Toney firing in a volley from Bryan Mbeumo's free-kick, but they had no answer to Neves' goal.
Wolves almost added a third goal in stoppage time when substitute Adama Traore thrashed the ball in at the near post, but his effort was ruled out for offside following a VAR check.
The game ended with Brentford manager Thomas Frank being shown a second yellow card for remonstrating with the referee as his promoted team slumped to their fourth successive league defeat.