Inter looked on course for a fourth consecutive trophy in the tournament after goals from Lautaro Martinez and and Mehdi Taremi either side of the break in Saudi Arabia.
But in a repeat of their 2-1 come-from-behind win against Juventus in the semi-final Milan returned transformed after the break.
To add to the Inter's woes the reigning Serie A champions lost Hakan Calhanoglu to a muscular injury just after half an hour with Kristjan Asllani coming on in place of the Turkish midfielder.
Theo Hernandez revived AC Milan hopes with a free kick after 52 minutes as they chased a first trophy under new coach Sergio Conceicao.
US winger Christian Pulisic grabbed the equaliser with 10 minutes to go with English forward Abraham sealing the winner after 93 minutes to give his side the trophy for the eighth time and first since 2016.
Three-time defending champions Inter had dominated Atalanta 2-0 on Thursday in the Super Cup semis staged in Saudi Arabia for the third year in a row.
AC Milan's eighth Italian Super Cup trophy moves them equal with Inter Milan and behind Juventus who have won the tournament a record nine times.
