Serie A: Sampdoria 0 Inter 4
Drama was expected at the Stadio Comunale Luigi Ferraris as coaches Walter Mazzarri and Sinisa Mihajlovic faced their former clubs.
There was also the small matter of Icardi going head-to-head with Maxi Lopez following the much-publicised tension between the two, surrounding the current relationship between the goalscorer and the Sampdoria man's former partner.
And Sunday's clash did not disappoint as Icardi opened the scoring in the 13th minute, with his provocative celebration setting the tone for a fiery first half in which Sampdoria were reduced to 10 men.
Sampdoria had a great chance to equalise just five minutes later but Inter goalkeeper Samir Handanovic kept out Lopez's penalty.
More tension followed as Eder – initially booked for simulation – was shown two yellow cards in quick succession for his part in a melee that saw him clash with Handanovic.
Walter Samuel doubled Inter's lead on the hour-mark before further goals to Icardi and Rodrigo Palacio helped the visitors move to fifth, following Parma's 1-1 draw at Bologna.
Icardi gave Inter the early lead when he volleyed Palacio's cross past the helpless Angelo Da Costa.
The striker's decision to cup an ear at home fans saw him booked but Sampdoria missed a golden chance to draw level from the penalty spot.
The spot-kick – conceded when Andrea Ranocchia brought down Daniele Gastaldello – was well saved, with Handanovic moving to his right and saving to keep his side in front.
Sampdoria were dealt a further blow with Eder's dismissal, as the Brazilian was adjudged to have dived following a Samuel challenge.
The aftermath was messy as several players tangled, but it was Eder's contact with the face of Handanovic that saw him given his marching orders in the 20th minute.
Sampdoria kept pressing, as Handanovic kept out a curling Lopez effort and Gianluca Sansone's free-kick, and the goalkeeper's stellar form continued as he denied Roberto Soriano just before the interval.
Handanovic's work would prove crucial as Samuel effectively sealed Inter's win 15 minutes into the second half.
The Argentina defender headed in Hernanes' corner and just three minutes later, Icardi kept cool to roll the ball home from a tight angle.
There was no big celebration on this occasion, but the game was already won, with Palacio capping the fine performance with a composed finish 11 minutes from time.
Palacio played a neat one-two with Ricky Alvarez and then strode unopposed into the Sampdoria penalty area, before slotting past Da Costa, as Inter registered their first win in five league matches, keeping them on course for a UEFA Europa League berth.