A frantic first half saw plenty of chances at both ends, and Michael Carrick’s side found the breakthrough thanks to Casemiro’s 11th-minute header.
Benjamin Sesko doubled the Red Devils’ lead in the 43rd minute, finishing well after being picked out by Bruno Fernandes, who registered his 19th Premier League assist of the season.
After spurning several glorious chances, Brentford got themselves on the scoresheet late on when Mathias Jensen lashed a wonderful strike in off the post, with Mikkel Damsgaard then seeing a header saved by Senne Lammens.
United are now 11 points clear of sixth-placed Brighton and Hove Albion with four Premier League games remaining, and their Champions League qualification could be rubber-stamped this coming weekend when they host fourth-placed Liverpool at Old Trafford.
Brentford remain ninth, one point off the European places.
How the match unfolded
The hosts should have gone ahead when Kobbie Mainoo brilliantly teed up Amad Diallo after a slaloming run, but Sepp van den Berg was on hand to deflect the shot off target.
Harry Maguire then went close from Fernandes’ corner, but that duo soon combined for United’s opener.
Fernandes’ delivery was met by Maguire, who headed to the back post, where Casemiro nodded in for his ninth Premier League goal of the season.
Brentford had their chances to equalise, with top scorer Igor Thiago squandering three great chances, and the Bees were made to pay when Fernandes – who is now just one shy of matching the single-season record for Premier League assists – picked out Sesko. The striker sat down Nathan Collins before rifling home to cap a brilliant counter-attack.
A tactical change from Carrick stalled Brentford after the break, but the visitors went close when Dango Ouattara headed against the woodwork from point-blank range.
Jensen did, however, provide a nervy finish when he spectacularly finished from 25 yards out in the 87th minute, but United were able to see out the victory despite a late wave of Brentford pressure.
