Argentina striker Diego Milito finished coolly on 57 minutes after great work from compatriot and captain Javier Zanetti to leave team-mates in tears at fulltime and coach Jose Mourinho pointing to the sky.
Second-placed AS Roma won 2-0 at Chievo thanks to Mirko Vucinic and Daniele De Rossi and would have been champions had the final games of the season finished at halftime.
As it was Inter topped the table on 82 points, two above Claudio Ranieri's side, and next meet Bayern Munich in Saturday's Champions League final in Madrid having also won the Italian Cup by beating Roma this month.
Sampdoria took the fourth and final Champions League qualifying spot with a 1-0 win over Napoli.
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