The 18-year-old winger put United ahead, winning the ball back near the Liverpool box before producing a composed finish.
Diallo made two further promising runs into the area in the first half but could not capitalise, as United let a 2-0 lead slip before half-time.
However, he helped his side ease to a high-scoring win in the end, although striker Joe Hugill was the star of the show with four goals.
He had five attempts on goal in total, hitting the target three times, as the Red Devils enjoyed a high-scoring triumph.
Diallo completed a move to Old Trafford this month after an agreement had been reached with Atalanta in the previous transfer window.