The 39-year-old Argentine began his Inter career 17 years ago, playing in a 1-0 Serie A win over Vicenza on August 27, 1995, after joining from Banfield, an unfashionable Buenos Aires club.
Zanetti's fellow Argentines Esteban Cambiasso and Rodrigo Palacio scored Inter's goals in the playoff round first leg.
Thirty matches were played on Thursday involving teams ranging from five-times European champions Liverpool to Neftchi Baku from Azerbaijan.
Neftchi achieved a 1-1 draw at home to APOEL Nicosia, who reached the quarter-finals of the Champions League last season.
Russian club Anzhi Makhachkala, who have splurged millions on players like Cameroon forward Samuel Eto'o and Dutch coach Guus Hiddink [ Images ], beat AZ Alkmaar 1-0 with a second-half goal from Ivorian forward Lacina Traore.
The match was played in Moscow [ Images ] after UEFA prevented Anzhi from playing at their base in the violence-plagued Dagestan region for security reaons.
Norway's Tromso, based inside the Artic circle, produced a shock 3-2 win over Serbia's Partizan Belgrade.
Athletic Bilbao, beaten finalists last season, trounced HJK Helsinki 6-0 and a 78th-minute own goal by Andy Webster gave Liverpool a 1-0 win at Hearts.
Aritz Aduriz and Markel Susaeta scored twice each for Athletic with Inigo Perez and Andoni Iraola sharing the others.