The hosts took the lead in the fourth minute when Mateo Kovacic's strike deflected into the path of Mauro Icardi and, after seeing his initial effort saved by the keeper, the striker followed up to slot the ball home.
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Sassuolo came close to a response moments later as Francesco Magnanelli fired in a strike from range that went just over the top corner.
On the half-hour mark, Inter made it three when Icardi picked up the ball just outside the box before bending a low strike into the bottom corner.
With two minutes of the first half left to play, the hosts further extended their lead when Osvaldo tapped home Dodo's pull back from close range.
Inter continued to dominate after the break and Icardi completed his hat-trick with his side's fifth goal in the 53rd minute by latching onto Kovacic's through ball to fire a shot past the keeper.
The Nerazzurri further compounded their opponents' misery in the 73rd minute as Fredy Guarin unselfishly squared the ball for Osvaldo to tap in for his second of the match.
Less than a minute later, Inter scored their seventh of the afternoon through Guarin, who curled a strike from the edge of the box into the corner past Consigli to complete the rout.