The breakthrough came from Norgaard in the 35th minute, before Toney's third Premier League goal of the campaign secured a vital three points for the Bees in their battle to stay out of the relegation zone.
Brentford are now on 25 points from 23 league matches this season, which has left them 14th in the table, while Wolves sit 10th, boasting 32 points from their 24 matches this season.
The visitors were much the brighter side in the early exchanges, with Wolves goalkeeper Jose Sa needing to be at full stretch to keep out Neal Maupay on two separate occasions.
The home side had a chance of their own in the 14th minute through Matheus Cunha, but his effort was saved by Brentford goalkeeper Mark Flekken.
Nathan Collins then passed up a huge chance for Brentford in the 21st minute, with the defender firing wide from close range when it looked easier to score, before Mathias Jensen missed the target with an ambitious effort in the 26th minute.
Brentford's pressure finally paid off in the 35th minute of the contest, with Norgaard's close-range header from a corner making the breakthrough at Molineux.
A brilliant save from Flekken prevented Pedro Neto from levelling the scores in the 44th minute, and Wolves then had a goal disallowed early in the second period, with Craig Dawson's header chalked off for offside.
Flekken was again called into action before the hour to push away a dangerous cross from Neto, and Brentford resisted more pressure in the spell that followed before scoring a second in the 77th minute.
Toney was at it again, with the forward making it three goals in four games since his return by finding the bottom corner with a first-time finish off a cross from Vitaly Janelt.
Wolves had a couple of opportunities to register in the latter stages, but Tommy Doyle missed the target with a powerful drive, before Matt Doherty headed wide of the post, and it was a deserved victory for Brentford, who managed to bounce back from successive losses to Tottenham Hotspur and Manchester City.
The hosts, though, were ultimately unable to build on their success at Chelsea last time out, with Gary O'Neil's side losing for the 10th time in the league this season.