Julio Cruz also struck for Inter before breaking down with a calf strain in the first-half. L'Imperatore was in good form and, when Amantino Mancini was felled inside Bari's area, converted a powerful penalty.
It was Adriano's first goal since returning to the club from his six-month loan spell at San Paolo.
"I know that I must remain calm and continue working hard. Preseason has been very positive, I've worked hard and well," said the Brazilian.