The Bosnian international has been playing up front for Simone Inzaghi's squad while both Romelu Lukaku and Joaquin Correa are out injured, and he showed that he still has the quality to fill the role.
Sassuolo took the initiative in the first 15 minutes, chasing their third league win in a row. Inter tried to create room in the midfield but had trouble with a well-coordinated Sassuolo defence playing high up the field.
Dzeko put Inter in front in the 44th minute when the ball bounced to his feet from a corner and he volleyed it in.
Sassuolo were the better team for most of the second half and pressured Inter, looking for weak points in the defence for an equaliser.
After several half chances, Sassuolo's Davide Frattesi equalised in the 60th minute when, standing unmarked, he volleyed in a cross from Rogerio. Inzaghi's expression of horror neatly summed up the failure of his side's defence to mark the Italian international.
The goal shocked Inter, and they moved into a higher gear at the end of the game. Sassuolo keeper Andrea Consigli made a world-class save in the 75th minute when he tipped the ball out of harm's way after a Lautaro Martinez header.
Only a minute later, however, a cross from substitute Henrikh Mkhitaryan into the box found Dzeko, who secured the win with a controlled header.
Inter are seventh in Serie A on 15 points having played one game more than the teams above them, and they are five points behind leaders Napoli. Sassuolo are in ninth place.