Mepham, who celebrated his 19th birthday on Saturday, scored a first-half wonder strike in the Griffin Park friendly as United went down 2-0 inside the first 25 minutes after Herson Alves headed in the second.
The game looked to be over once Mepham scored again after half time but The Red’s clawed two goals back in the second half.
Goals from Joe Riley and defender Sean Goss made for an exciting finale but United were unable to salvage a draw in their first game following the departure of former boss Warren Joyce to Wigan Athletic.
In a first half where Brentford had the best chances, players like former Arsenal left-back Ilias Chatzitheodoridis caused several problems for United’s defence.
Mepham’s 12th minute opener was a stunning 30-yard strike from outside the box that capitalized on the Bees superiority.
Brentford continued to break with pace and Alves scored ten minutes later with a header for the second goal in the 22nd minute from Reece Cole’s cross.
United’s first shot on goal came in the 35th minute as Matthew Willock’s 20-yard effort was palmed away by Bees keeper Dominic Kurasik.
The second half began with a flurry of United chances from Goss and Riley before Mepham scored his second on 60 minutes against the run of play.
Manchester United looked resurgent after another strike from outside the box saw Riley score to give hope to the away side on 63 minutes.
Defender Goss, in his second game after returning from a long injury absence, scored from outside the box, as his 70th minute goal pegged United back to 3-2.
In an erratic period of added time United had several chances to steal a draw with former Brentford winger Josh Bohui pulling his shot wide in the final moments to allow the Bees a home victory.