A 4-0 victory to seal a fourth consecutive Coppa Italia. So absolute is Juventus’s domination of the domestic scene these days that they can apparently even afford themselves self-referential scorelines. No team had ever won so many consecutive editions of this tournament. Then again, that was already true last year.

Milan were the opponents whose dreams they shattered this time at the Stadio Olimpico. Before kick-off you could take your pick of the storylines: from Leonardo Bonucci seeking to get one over on his former team to the duel-at-a-distance between a nation’s greatest goalkeeper, Gigi Buffon, and his heir apparent, Gianluigi Donnarumma. Over 90 minutes we were reminded there is only one winning narrative in Italian football these days, and it is written by the team in black and white.

Or perhaps it would be more apt to speak of a game played in 20 minutes, not 90. That was all it took for this final to transform from a tense but uneventful affair into a lopsided rout. Milan had played with justifiable caution throughout the first half and succeeded in keeping things tight. As soon as they fell behind, they fell apart.

Three of Juve’s four goals were gifted to them. Donnarumma allowed a Douglas Costa shot to slip through his fingers for the second, before dropping a ball at Mehdi Benatia’s feet for the third. The fourth was an own goal by Nikola Kalinic. Only the opener, headed in by Benatia from a corner, came without a Milan assist.

This was a day of redemption for the Moroccan, after a month in which he became the scapegoat for a side that were in danger of throwing this season away. It was he who gave away the penalty that killed Juventus’s hopes of a sensational Champions League comeback in Madrid. Benatia then lost Kalidou Koulibaly for Napoli’s winner at the Allianz Stadium, a goal that briefly reignited the Serie A title race.

He did not help himself with his remarks at the end of the Madrid defeat, likening the penalty award to a “rape” and subsequently engaging in a war of words with the comedian Maurizio Crozza – who called him out on his use of language (while unhelpfully extending the sexual metaphor in his own response). Massimiliano Allegri, perhaps sensing the player was distracted, dropped him against Bologna and Inter.

The manager knows very well, though, how important Benatia has been. It would be easy to kid ourselves that Bonucci’s departure made no impact on a team that have continued to sweep all before them, but the reality is that there were times in the early part of this season when Juventus looked far less assured. They began the campaign by shipping three goals in a Supercoppa defeat to Lazio. Five separate opponents had put two or more past them by the end of October.

Medhi Benatia puts Juventus ahead in the Coppa Italia final, a goal that opened the floodgates. Photograph: Angelo Carconi/EPA

It was only from late November that things really started to come together, Juventus conceding only a single goal in 16 games across all competitions. Giorgio Chiellini was injured at the start of that sequence. Benatia had served as cover for the famous BBC during much of his first season in Turin, but his cool reading of the game and capacity for playing the ball out from defence had now become indispensable.

That is just another example of how this Juventus team have continued to evolve and adapt, the first-team squad subject to constant change over the four years of Allegri’s leadership, yet always capable of getting results when it matters. Milan, for all their vast expenditure last summer, remain a very long way behind.

Defeat here means their spot in Europe next season is still not guaranteed. They sit sixth in Serie A, one point ahead of Atalanta and three ahead of Fiorentina – both of whom they face in the remaining two weeks. Even falling to seventh would be painful, obliging them to begin Europa League qualifying in July.

Whether Donnarumma will be around to make the next step with them is open to doubt. He looked to be on the verge of tears as Bonucci sought to console him at full-time. Buffon offered his namesake a kiss and a pat on the cheek that may have been a little harder than he intended.

Then the older man jogged off to enjoy the moment with his team-mates. Corks were popped, champagne sprayed and Allegri thrown up in the air. As Buffon told it late last year: “I drink little, but I celebrate quite a bit.”

For Juventus, winning is a habit. They ran through this entire Coppa Italia without conceding a goal. The only question now is whether they complete a fourth consecutive domestic double on Sunday at this same stadium, away to Roma, or leave that for the final weekend, when they host relegated Verona in Turin.

The story is already written. All that remains is to see if Juventus can give it an end as fitting as the scoreline they produced on Wednesday night.