Ciro Immobile scored the deciding spot kick for Super Cup debutants Bologna after Alessandro Bastoni, Nicolo Barella and Ange-Yoan Bonny all missed for Inter.
Lews Ferguson and Jonathan Rowe also scored for Bologna, while Lautaro Martinez and Stefan de Vrij converted for Inter.
Bologna take on Napoli on Monday after the Italian champions secured a 2-0 victory over AC Milan on Thursday.
Inter struck early on at King Saud University Stadium, as Alessandro Bastoni swung in a cross to the back post in the second minute where Marcus Thuram arrived at full stretch to fire into the net.
However, despite Inter's dominance, Bologna were awarded a penalty in the 35th minute following a handball from defender Yann Bisseck.
Forward Riccardo Orsolini made no mistake from the spot to bring the teams back on level terms.
Inter thought they had a penalty of their own shortly before the hour mark due to a foul, only for a VAR review to overturn the decision.
Despite chances at both ends, neither side could find a winner, sending the match straight to a penalty shootout, where Immobile proved decisive.
The Italian Super Cup is played between the winners and runners-up of last season's Serie A and Italian Cup, with all the games in Saudi Arabia.
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