Brazilian midfielder Hernanes hit his maiden goal for Juve to give the hosts a half-time lead but it took until Simone Zaza's 80th minute strike, after he had replaced Alvaro Morata, for the title celebrations to really begin.
Juventus win fifth successive Serie A title after Napoli loss
Juventus, now 15 points ahead of second-placed Napoli before they host Atalanta on Monday, had secured a record-equalling fifth consecutive Serie A crown last Monday when Roma defeated Napoli 1-0 in the capital.
After a week of celebrations, it was far from sterling stuff from the Turin giants but Allegri said: "It wasn't a great game, but the tension had dropped off a little following our title celebrations last week.
"But now it's important for us to keep our focus with a view on the Italian Cup final against Milan."
Allegri now has three Serie A titles on his coaching CV having steered AC Milan to the 'scudetto' in 2011, only to be sacked by the seven-time European champions following a 4-3 defeat to Sassuolo in January 2014.
In hindsight, it was probably the best thing to have happened to the 48-year-old coach, who led the Old Lady to a first Champions League final in 12 years in 2015 and stands on the verge of a second consecutive league and Cup double.
Serie A: Juventus within striking distance of title
Milan host Juve in the Cup final on May 28, and going on Sunday's respective performances the Turin giants will be odds-on to defend their trophy.
Crisis-hit Milan hit a new low by dropping to seventh after fighting back from 3-1 down to secure a 3-3 San Siro draw with Frosinone.
Milan, who sacked coach Sinisa Mihajlovic three weeks ago and replaced the popular Serbian with youth team coach Cristian Brocchi, are now even further out of contention for a place in next season's Europa League -- a short order for a team that once rubbed shoulders with the giants of European football.
Sassuolo, 1-0 winners against relegated Verona, replaced Milan in sixth place, which will be awarded a Europa League spot from the Italian Cup final if Juventus, already qualified for the Champions League, beat Milan later this month.
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Sassuolo coach Eusebio Di Francesco even had the gall to warn: "We've always been chasing Milan, and sometimes those in pursuit are at an advantage. Now we have to focus on our next two games, they will be decisive."
After a dismal draw with relegation-haunted Carpi and a shock defeat to basement side Verona, Milan were looking to make amends.
But frustrated fans largely stayed at home amid reports club owner Silvio Berlusconi is on the verge of selling a majority stake to a Chinese consotrium, and their decision was largely vindicated.
Luca Paganini beat 'keeper Gianluigi Donnarumma from the edge of the box after two minutes and Frosinone doubled their lead on the stroke of half-time when Oliver Kragl's free kick beat Donnarumma at the near post.
Balotelli's penalty was parried by Francesco Bardi just after half-time although Carlos Bacca reduced arrears minutes later.
Although Federico Dionisi pounced on Alex's error to put the visitors 3-1 up, Luca Antonelli came off the bench to score an overhead kick with his first touch on 74 minutes.
In a desperate finale, Milan avoided total humiliation when Menez struck from the spot after Vasyl Pryima handled in the box.
Brocchi faced a social media backlash, especially after he attempted to paint the performance in a positive light.
"Today, compared to our games against Carpi and Verona, we created more than 20 scoring chances, we hit the woodwork twice and missed a penalty. That's why I'm not disappointed," he said.
In Sunday's late game, an away win at Lazio would secure fourth place and a Europa League spot for Inter Milan, who are currently four points ahead of Fiorentina in fifth.
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