After last week’s shock 2-0 defeat at Chievo, Inter were keen to make amends in their first game of the campaign at the San Siro, where new signing Joao Mario was presented to fans minutes before kick-off.
But Inter, who were busy in the summer transfer market following their recent takeover by Chinese tycoon Zhang Jindong, are still a work in progress under new coach Frank De Boer.
Andrea Rispoli gave Palermo the lead before Icardi’s 72nd-minute leveller.
Elsewhere, Fiorentina made amends for last week’s 2-1 defeat to Juventus with a 1-0 win over Chievo as Carlos Sanchez headed a 29th-minute winner for his maiden goal in Serie A.
At Sampdoria, Ivorian teenage defender Franck Kessie hit his third goal in two games for Atalanta, but the hosts were level from Fabio Quagliarella’s 35th-minute spot-kick and clinched a 2-1 win thanks to Edgar Barreto’s goal on the stroke of half-time.
Sassuolo beat Pescara 2-1 and Udinese were 2-0 winners at home to Empoli.
In Saturday’s other game, Napoli beat AC Milan 4-2 with Polish international Arkadiusz Milik, signed as a replacement for Juventus-bound Gonzalo Higuain, scoring a brace.