Both Inter and Sassuolo drew their opening fixtures, but the win never looked in doubt for the home side after Icardi netted his first in the fourth minute at San Siro.
Mateo Kovacic played a key role in setting up the opener and got his own name on the scoresheet in the 21st minute.
Icardi curled home a superb third after 30 minutes and Pablo Daniel Osvaldo's first league goal for Inter made it 4-0 at the interval.
The hat-trick was complete in the 53rd minute when Icardi smashed in a left-footed strike before Sassuolo's Domenico Berardi saw red for an elbow on Juan Jesus.
Osvaldo scored his second to make it six in the 72nd minute and Fredy Guarin completed the rout two minutes later.
The result comes almost exactly 12 months after Inter hammered Sassuolo by the same scoreline on the road last season.
Marco Andreolli took the place of the suspended Nemanja Vidic in the Inter defence, while Osvaldo joined Icardi in attack.
And it did not take long for the home side to break the deadlock, with Icardi bundling the ball home in the fourth minute.
Kovacic tried his luck from the edge of the penalty area, but his shot deflected into the path of Icardi, who eventually found a way past Andrea Consigli after the debutant goalkeeper saved his initial effort.
Berardi's deflected cross just evaded Nicola Sansone as Sassuolo chased an equaliser, and they were swiftly punished for that squandered opportunity.
Kovacic, who scored his first goals for Inter with a hat-trick in the 6-0 UEFA Europa League win over Stjarnan last month, opened his Serie A account when he slid the ball past the advancing Consigli with the outside of his boot in the 21st minute.
And the goals just kept on coming for the home side as Inter surged 3-0 ahead.
Icardi picked up the ball just outside the box on the half-hour mark and had time to compose himself before curling into the bottom right-hand corner of the net.
Osvaldo then made it four before half-time, side-footing home from six yards after Consigli had denied Dodo.
The on-loan Southampton striker could have put Inter five up three minutes into the second half, but sent his effort narrowly wide of the left-hand post.
However, Icardi netted his third soon after – powering home after getting on the end of a Kovacic throughball.
Sassuolo's dismal display got even worse when one of their main goal threats – Berardi – saw red for an inexcusable off-the-ball elbow on Juan.
Guarin then came off the bench to tee up Osvaldo for his second in the 72nd minute before the goalscorer turned provider as the Colombian fired in an effort off the post soon after.