But Inter was immediately level when Icardi latched onto Fredy Guarin's through ball and cut across Mario Yepes before firing into the bottom left corner. To celebrate he held up a T-shirt dedicated to his girlfriend Wanda Nera, the ex-wife of former Sampdoria teammate Maxi Lopez.
Inter should have sealed the match in the second half but Guarin smashed a shot off the crossbar and Rodrigo Palacio sent a glancing header onto the left upright.
Both sides could have snatched the win. Inter's Jonathan cleared off the line three minutes from time before chipping the ball off the underside of the crossbar at the other end.
Atalanta secured the result when Bonaventura was left completely unmarked at the far post to head a free kick between Handanovic's legs.
Parma maintained its charge toward a European spot as it extended its club record unbeaten run to 17 matches.
Genoa took the lead against the run of play in the 21st when Isaac Cofie drilled Moussa Konate's through ball across Parma goalkeeper Antonio Mirante.
Parma leveled 10 minutes later. Genoa failed to deal properly with a free kick and Ezequiel Schelotto fired a powerful shot into the top corner.
Verona looked on course for a European spot at the turn of the year but has only won one of its past 11 games and fell to a third consecutive loss.