Andreas Pereira scored the third and undoubtedly best volley of the night in the second half, which restored United's lead.
Ole Gunnar Solskjaer's men were a goal to the good after twelve minutes with thanks to Anthony Elanga. Elanga scored his second in as many games when he put United ahead early in the first half with a well-taken volley into the bottom corner.
The newly-promoted Brentford bounced back with a stunning goal of their own through Shandon Baptiste. The midfielder fired in the equaliser with a volley off the underside of the crossbar past Tom Heaton.
Story of the game
Similarly to the Queens Park Rangers fixture just four days ago, United started on the front foot and took the lead shortly into the game.
Aaron Wan-Bissaka - a player who has been criticised for his attacking play recently - found space down the right and put in a cross slightly behind Elanga who still managed to volley it past a diving David Raya.
That was the 19-year-old's second goal in two games after scoring against QPR at the weekend.
Brentford did not take long to respond, and they responded in some style. Baptiste struck the ball from outside the box with a sliced volley which perfectly curled away from Heaton to hit the underside of the crossbar and go in.
United's best chance to retake the lead came just before half-time with an excellent team move. It started with a determined run from Wan-Bissaka who then released the ball to Elanga. The Swedish striker got the ball caught underneath his feet but managed to get the ball out to Greenwood on the left wing. Greenwood then found Jesse Lingard on the edge of the box unmarked, but his shot was deflected wide for a corner.
The second half got underway and United were back in the lead after an unbelievably well-struck volley by Pereira. It was a goal of pure class, one that United legend, Paul Scholes, would have been proud of.
The United midfielder spent last season on loan at Lazio but returned to the club this summer. Whilst the volley was probably not enough to convince Solskjaer he is worth keeping at the club, the volley may have teased a few interested teams into making an offer.
After messing around with the ball in his own box, the Brentford goalkeeper lost possession and left his goal unattended. Lingard pounced and struck the ball first-time from distance but the effort sailed over the bar.
Some terrible defending by Diogo Dalot allowed Mbeumo to drive into the box, cut onto his left foot and slot past Heaton into the far corner to make it 2-2 with ten minutes to play.
United have their fourth pre-season fixture scheduled on Saturday, where they face Preston North End.