The Red Devils entered the half-time interval behind after Ethan Pinnock's bullet header from a Mikkel Damsgaard corner in the fifth minute of stoppage time gave Brentford a slender advantage.
However, Erik ten Hag's side burst out of the blocks after the break and Alejandro Garnacho scored just 89 seconds after the restart to restore parity, before Rasmus Hojlund scored a superb chipped goal over Mark Flekken to put the hosts in front just after the hour mark, and they eventually held on to claim three crucial points.
Here, Sports Mole provides player ratings from Man United's victory against Brentford.
Man United player ratings vs. Brentford: Garnacho, Hojlund on target for Red Devils
GOALKEEPER
Andre Onana - 7/10
A solid performance from Onana between the sticks. He looked confident and composed with the ball at his feet and made a superb save at full stretch to deny Norgaard from distance in the first half.
DEFENCE
Diogo Dalot - 6/10
Dalot defended reasonably well and got forward at times from right-back, but he was at fault for Brentford's opener, allowing Pinnock to have a free header from a corner on the stroke of half time.
Matthijs de Ligt - 7/10
De Ligt was in the wars early on and batted through the 90 minutes with a blooded head following a collision with Schade's knee. The Dutchman was off the pitch receiving treatment when Brentford scored at a corner, but he impressed from a defensive perspective once his issue was sorted.
Jonny Evans - 7/10
Reports prior to kickoff suggested that Ten Hag was considering using Jonny Evans at left-back, but the Northern Irishman continued at centre-back after a standout defensive display in that position against Aston Villa last time out. He impressed again, and the Old Trafford faithful were singing his name for large sections of the second half.
Lisandro Martinez - 7/10
Martinez was tasked with operating at left-back and after a tricky opening half-hour or so up against Mbeumo, the Argentine put in a gritty defensive performance, winning the majority of his duels and got forward at times down the left.
MIDFIELD
Casemiro - 7/10
In the absence of injured midfielder Kobbie Mainoo, Casemiro was recalled to the first XI and impressed for the majority of the match, making four key passes, four clearances, winning seven ground duels and 100% of his aerial duels.
Christian Eriksen - 6/10
Eriksen blazed a glorious chance from six yards out over the crossbar - although the goal would not have stood due to a foul in the build-up - and had few flashes of quality. The Dane did start the move that led to Hojlund's goal, though.
Bruno Fernandes - 6/10
An underwhelming display, and not the first of this season, from Fernandes, who was dispossessed a few times and struggled to make the desired impact in the final third, until he produced a cute assist flicked towards Hojlund for his goal.
ATTACK
Alejandro Garnacho - 8/10
Garnacho lacked a cutting edge in the final third and wasted a number of decent opportunities in the first half, but he made up for it big time with a man-of-the-match display after the break. The Argentine was excellent throughout the second half; he got in behind on the left on several occasions and scored arguably the most difficult of all the chances presented to him.
Rasmus Hojlund - 8/10
Hojlund was a physical presence up front while battling with Pinnock and Collins, and was also skilful at times with the ball at his feet, before netting a cool, clever and composed goal dinked over Flekken.
Marcus Rashford - 7/10
Playing for the majority of the match on the right flank, Rashford could have made more of opportunities presented to him, particularly in the first half, but he provided a marvellous curling assist for Garnacho from the edge of the area.
SUBSTITUTES
Joshua Zirkzee - 5/10
Held the ball up on occasions, but he was rarely involved after replacing Hojlund with 16 minutes plus stoppage time remaining.
Manuel Ugarte - N/A
Replaced Casemiro in the 88th minute.
Victor Lindelof - N/A
Replaced Jonny Evans in the 89th minute.
Noussair Mazraouri - N/A
Replaced Alejandro Garacho in the 91st minute.
Brentford player ratings vs. Man United: Pinnock, Flekken star for Bees as Mbeumo struggles
GOALKEEPER
Mark Flekken - 8/10
Flekken nearly gifted Hojlund a first-half opener after fumbling a header from Martinez, but he made up for it - albeit conceding twice - after making a total of nine saves. Without his interventions, Man United would have won more handsomely.
DEFENCE
Sepp van den Berg - 5/10
Looked nervous at times both in and out of possession and endured some difficult moments up against Garnacho. Lost possession a total of 11 times in the 90 minutes while playing at right-back.
Ethan Pinnock - 8/10
Was a solid showing at the back for Brentford's No.5 throughout the contest and scored a thumping header past Onana to put the Bees in front. A standout performer despite coming away on the losing side.
Nathan Collins - 6/10
Collins was fairly solid at the back, but he gave the ball away which led to Man United's second goal and struggled at times in possession.
Kristoffer Ajer - 6/10
Ajer was solid for much of the contest at left-back and made a couple of nice runs forward either on the left on in central positions. Was booked for a late lunging challenge on Hojlund on the counter-attack.
MIDFIELD
Vitaly Yanelt - 6/10
Solid but nothing spectacular from Yanelt. He got stuck in when required and sprayed some nice passes about from central areas. Was subbed off with 15 minutes remaining.
Christian Norgaard - 6/10
Norgaard was unfortunate not to score from the edge of the area with a superb curling shot saved at full stretch by Onana. Similarly to Yanelt, a solid performance from the Dane, but nothing spectacular.
Mikkel Damsgaard - 7/10
Damsgaard operated in a slightly more advanced role compared with Yanelt and Norsgaard and was an energetic presence in Brentford's midfield. He also produced a brilliant delivery from a corner headed home by Pinnock.
ATTACK
Bryan Mbeumo - 6/10
Mbeumo was unsurprisingly oozing with confidence having made a bright start to the campaign, but his lively start at Old Trafford fizzled out and he was unable to test Onana between the sticks.
Kevin Schade - 6/10
Schade had a couple of half-decent chances to score either end of the first half, but he was cut a frustrated figure up front for much of the match.
Keane Lewis-Potter - 6/10
Posed a threat at times when driving forward at Man United's backline, but he lacked an end product and faded as the second half went on.
SUBSTITUTES
Yoane Wissa - 5/10
Replaced Lewis-Potter with 25 minutes remaining and was presented with one opportunity to run in behind, but he was unable to take it.
Fabio Carvalho - 5/10
Came on for the final 16 minutes plus stoppage time, but was unable to make the desire impact in the final third.
Yegor Yarmolyuk - 5/10
Also came on for the final 16 minutes plus stoppage time and his only notable action was a blazed shot over the crossbar in the closing stages.
Mads Roerslev - N/A
Replaced Van den Berg in the 86th minute.