Inter remain second in the table, three points behind Juve who beat Fiorentina earlier on Sunday.
Christian Eriksen, Ashley Young and on-loan Chelsea winger Victor Moses made their league debuts for the Nerazzurri.
But it was Lukaku who ensured victory, scoring with a close-range shot before adding his second with a penalty.
The former Manchester United forward has now scored 16 league goals since moving to Italy last summer and has scored 20 for Inter in all competitions.
He was helped by some poor goalkeeping by the hosts’ Juan Musso for his first, then by on-loan United forward Alexis Sanchez for his second – with the Chilean winning the spot-kick from Musso.
Antonio Conte’s side had drawn their three previous league games 1-1 . They are next in action when they host their rivals, AC Milan, in the Milan derby on Sunday, 9 February (19:45 GMT)