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Allegri became the first coach to win the Coppa Italia five times after Sven-Goran Eriksson and Roberto Mancini lifted the trophy on four occasions.
With eight games left to play in this season, the decision lifts Juventus from seventh to third in the Serie A table - with 59 points.
Dybala will become Roma's fourth signing of the transfer window after the arrivals of midfielder Nemanja Matic, goalkeeper Mile Svilar and defender Zeki Celik.
Pogba, who left United when his contract expired last month, has signed a four-year contract with Juventus that will tie the 29-year-old down with the Turin club until June 2026.
Having fallen before the quarterfinals against Olympique Lyonnais and Porto in the previous two seasons, in-form Juventus, who had lost just once in their last 21 matches in all competitions, were firm favourites to progress.
Kerr showed skills more in keeping with the Australian Rules code she played as a child when she barged into the fan who had run onto the Kingsmeadow pitch late in Wednesday's game, leaving him in a heap on the ground.
Chelsea claimed a thumping 4-0 victory over Juventus.
Knowing they only needed a point against Zenit to be assured of a knockout-stage spot in Group H, Juve raced into a deserved early lead through Dybala, who hammered the ball into the roof of the net in the 11th minute.
The Portuguese superstar dedicates his Manchester United return to former boss Alex Ferguson.
Financial details of the transfer were not disclosed but British and Italian media reported United signed Ronaldo for 25 million euros.
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