Moutinho opened the scoring early in the second-half with a delightful finish using the outside of his boot from just inside the box. Ivan Toney then levelled the scores, but Moutinho was again involved just moments later to set up Ruben Neves whose curling near-post finish made the Bees suffer their fourth straight Premier League loss.
The result sees both sides remain in their respective positions in the Premier League table: Brentford in 14th, eight points clear of the relegation zone, and Wolves in 8th, still serious contenders in the fight for European qualification.
Story of the game
Coming into the match, Brentford head coach Thomas Frank made two alterations to his starting 11, with both Kristoffer Ajer and Rico Henry welcomed back into the fold having been benched against Manchester United in midweek to preserve their fitness.
Meanwhile, Bruno Lage was without arch marksman Raul Jimenez up front due to a calf niggle so Fabio Silva was entrusted up front instead, partnering Daniel Podence, though there was positive news to be found for the visitors in the return of Ruben Neves in midfield.
The first chance of the match fell Brentford's way as Henry initiated initiated a good move down the left which gave Vitaly Janelt the space to deliver a low cross in towards Sergi Canos, but the wing-back failed to make proper contact with the ball.
There was little to separate the sides in the opening exchanges, but the hosts were certainly asking more of their visitors' defence. On the 15-minute mark Bryan Mbeumo sent Toney through on goal with a cleverly disguised pass, but when the latter attempted to return the ball to the former it was cut out and Wolves cleared their lines
A nasty clash of heads between Henry and Mathias Jensen, both attempting to clear a Wolves long-ball, saw play stopped on the 20th minute mark with both players in need of medical treatment and a concussion assessment. The pair were withdrawn as a precaution with Brentford using up their two concussion substitutions for the match.
The break in play allowed Wolves to reset after an opening period in which they'd failed to asset themselves upon proceedings. Nelson Semedo had fire in his belly as he darted forward from the half-way line and sized up a shot at goal, but his effort blazed way over the target. The visitors were really struggling to break their hosts down here.
But play was soon halted again due to an 'unofficial drone' being sighted above the Brentford Community Stadium, with the players instructed to leave the field as per Premier League rules. Neither teams were really able to get going here and nor, it seemed, was the match itself.
It was a 19-minute stoppage all-in-all but, eventually, the drone was down and proceedings were able to resume — though such a bizarre occurrence was always likely to have some impact on the performance of both teams heading into the rest of the match.
Sure enough, the rest of the first-half was far off the average pace of a Premier League match as both sides attempted to warm themselves back up and regain their matchday mindsets; the drone was an unwelcome distraction and it was no surprise whatsoever to see the game remain scoreless at the break.
There was then a delay to the start of the second-half as referee Peter Bankes experienced technical issues presumably conceding his headset — ironic jeers greeted him as he finally entered the pitch after another stoppage uncalled for.
Wolves came out the blocks quicker than their opponents, and found themselves in front just — minutes into the half. Moutinho exchanged a slick one-two with Semedo, working his way into the area before summoning up a delicious finish with the outside of his right boot, giving goalkeeper Jonas Lossl no chance.
Lage's men had found their groove now; they nearly doubled their advantage when Leander Dendoncker made his way to the byline and crossed in towards Fabio Silva in the centre, but it was just to far in front of the teenager for him to get a touch on the ball.
With their visitors digging their heels in, Brentford were finding it increasingly difficult to work the ball into the box and create meaningful goalscoring opportunities — they nearly managed so when Toney exchanged a neat one-two with substitute Yoane Wissa to work space for the latter on the edge of the box, but his eventual effort was well over.
Bankes was having an eventful afternoon in charge of this one — on 70 minutes he sent off Toti Gomes for alleged serious foul play following a challenge on Ajer with Brentford through on goal but, after reviewing the footage on the monitor, the decision was overturned and Gomes awarded a yellow instead.
From the resultant free-kick, the Bees were level. Mbuemo floated a superb free-kick straight onto Toney's foot at the back-post and the striker finished brilliantly with a deft volley with such power that it nestled behind Jose Sa before the goalkeeper had the opportunity to react.
It didn't take long at all for the visitors to reinstate their advantage. Semedo had caused problems moments earlier with a fizzing cross from the byline, but the goal came when Moutinho laid the ball off for Neves on the edge of the box and powered in at the near post. Lossl had to do better, but it was a well-worked goal and an accomplished finish.
Given the pattern of the match, their equaliser earlier had come as something of a surprise; could Brentford claw themselves back again?
Well, as Wolves prepared to dig their heels in once again, chances were increasingly few and far between. Lage's side are markedly accomplished at seeing out results when they go ahead and today was no different, as they consigned Brentford to their fourth league defeat on the spin.
Takeaways from the match
Brentford fail to cause their visitors enough problems in attack
Toney's masterful goal came as a real surprise because, truth be told, Brentford didn't create enough today against a team that are more than happy to dig their heels in and play on the back foot.
They did well to work the ball to the edge of the box on a number of occasions but, all too often, that was where their attacks would be thwarted — that crucial final ball, and finish, is too often missing from Brentford's build-up play these days, and it's an issue Frank and his players will be keen to address.
The Moutinho effect
With his goal and assist proving decisive in the outcome of today's match, Moutinho proved once more why he is such a pivotal part of Lage's side. The latter was fairly simple but nonetheless expertly performed, while the former was a sumptuous finish
But Moutinho impacted Wolves in more intangible ways, too. The armband is worn by Conor Coady these days but the Portuguese midfielder is a de facto captain in his own right, constantly encouraging his teammates and setting an example both with and without the ball.
Difficult afternoon for Peter Bankes — to say the very least...
From having to overturn his own decision to dismiss Ajer to struggling to connect his microphone wiring as the players waited eagerly to recommence proceedings after the break, this was not Bankes' finest showing in the all-black kit. He may get some sympathy, and suffice it to say both sets of fans were less than impressed with his display.
Brentford: Lossl; Ajer, Jansson [c], Pinnock; Canos (Ghoddos 83'), Jensen (Baptiste 26') (Forss 79'), Norgaard, Janelt, Henry (Roerslev 25') (Wissa 57'); Mbeumo, Toney.
Unused subs: Fernandez, Stevens, Sorensen, Bidstrup.
Wolverhampton Wanderers: Sa; Kilman, Coady [c], Toti; Semedo, Neves, Dendoncker, Moutinho, Ait-Nouri; Silva (Adama 75'), Podence (Trincao 90').
Unused subs: Ruddy, Hoever, Marcal, Giles, Jordao, Cundle, Chiquinho.
Referee: Peter Bankes
Once the upcoming winter break is out of the way, Brentford return to action in the FA Cup on 5 February as they travel to Everton for the fourth round clash.