Lukaku has scored 15 goals in his last 13 games for Inter and Belgium, including 10 in nine this season.
Inter failed to have a shot on target in the first half of a league game for the first time since March 2019.
Lukaku played a one-two with substitute Nicolo Barella before scoring the opener and Danilo D’Ambrosio headed in Andrea Ranocchia’s corner.
Antonio Conte’s Inter have picked up 10 points from five games this season, two behind leaders AC Milan.
They overtake Atalanta, who lost 3-1 at home to Sampdoria earlier in the day.