The Belgian striker fired the visitors in front after 28 seconds and Inter soon raced away as a Roberto Gagliardini strike and Lukaku's second put them three up before the half-hour mark.
Substitute Lautaro Martinez scored with a neat finish after the break before Caprari notched his second to earn Pippo Inzaghi's side a consolation.
Benevento are on three points, thanks to their opening day comeback victory over Sampdoria.
Antonio Conte made seven changes to the side that beat Fiorentina 4-3, but Inter took the lead almost immediately when Lukaku swept home Hakimi's cross.
Two goals in three minutes ended the game as a contest by the 28th minute, as Gagliardini smashed a half-volley home before Lukaku tapped in his second.
Caprari pounced on a poor clearance from Inter goalkeeper Samir Handanovic to reduce the deficit, but Hakimi soon capitalised on hesitant Benevento defending to fire in.
Both sides were denied by the woodwork after the break as Gabriele Moncini clipped the post for the hosts and Gagliardini shot against the bar.
Inter substitute Martinez made it five with a curling effort, before Caprari's close-range finish ended the goal-fest.