But Huddersfield hit back with two tries in quick succession, with Brown finishing off the first from close range after starting a fine breakaway moments earlier.
And Cox showed his finishing prowess when he powered in a long range strike, which might have taken a deflection off Yuki Abe, to put the Di Matteo's men into the quarter-finals.
The downhill race on Sunday saw competitors plummet 550ft down the 1.75 mile (2.8km) boulder-strewn course before finishing at the bottom gondola station at the Nevis Range.
Berbatov sent a curling shot just wide and failed to match the quality of his and United's play with a finishing touch as he poked a Michael Carrick cross the wrong side of the post from close range.
But they had a horrendous first-half defensive performance and Joe Johnson was bad all game on offense, finishing with six points on 2-of-14 shooting, including 1 of 9 from 3-point range.
Ji-Sung scored with an effort from point-blank range after being the quickest to react after Friedel parried a Ronaldo free-kick and Solskjaer added the finishing touch to the win with his late strike.