Mandzukic gave the hosts a 12th-minute lead when he met Juan Cuadrado's cross at the back post to fire past Crotone goalkeeper Alex Cordaz.
Mario Mandzukic celebrated his 31st birthday by putting Juve in front and a stunning free-kick from Paulo Dybala made it 2-0 at the break.
Juve clinched the second prize of a potential treble haul as they wrapped up their sixth straight Serie A title, with a 3-0 victory over Crotone on Sunday.
Ahead of their final game at Bologna next week, Juve are now four points ahead of their closest challengers.
Crotone's loss, despite five wins and two draws in the last seven games, meant they were going to drop down to Serie B. It is only poor luck for the team as their fate depended on beating Juventus who had dropped only two points at home this season.
But the Calabrians were never likely to deny Juventus the well-deserved title celebrations, that had been put on hold last week when Roma stunned Allegri's men 3-1 at the Stadio Olimpico.
Luciano Spalletti's side won 5-3 in a thrilling game at Chievo on Saturday, while Napoli trounced Fiorentina 4-1 to keep the title race alive.
"Juventus" for the sixth time in a row won the Series A. this series of Analogues in the history of Italian football was not.
While Juve can now turn their focus towards the Champions League final against Real Madrid on June 3, Crotone will go into the final weekend with their Serie A status still uncertain.
Juventus wouldn't be in their current position without long-serving goalkeeper Gianluigi Buffon, who at 39 years old remains the bedrock, and captain of the Turin giants as they head towards a possible treble, and he heads towards an expected retirement following an eventual Italy campaign at the 2018 World Cup in Russian Federation.
Napoli are a further point behind in third, the Champions League playoff spot.
Gerard Deulofeu scored with a volley in the 69th, Keisuke Honda added a free kick four minutes later and Gianluca Lapadula redirected a cross from Mati Fernandez in added time.
Roma leveled shortly before the hour as El Shaarawy ran onto a Federico Fazio header from the halfway line and rounded Stefano Sorrentino, who rushed out to the edge of the penalty area, before depositing it into the empty net.