Antonio Conte's side needed two goals in the final three minutes to begin its campaign with a thrilling 4-3 win against Fiorentina, and while it found the net frequently again, this triumph was much more straightforward.
Lukaku scored twice in the opening 28 minutes, either side of Roberto Gagliardini's effort, before newly promoted Benevento pulled one back through Gianluca Caprari.
Yet Hakimi and substitute Lautaro Martinez also found the net as Conte comprehensively won the battle of the former Juve team-mates, despite a second Caprari goal late on.
Inter had fallen behind within three minutes against Fiorentina last Sunday (AEST), but this time it raced out of the blocks.
A long raking pass from Aleksandar Kolarov reached Hakimi and, after a one-two with Alexis Sanchez, he crossed for Lukaku to find the net just 28 seconds in.
Hakimi, making his full debut for the Nerazzurri, was then involved in his side's second when his deep delivery found Ashley Young, whose lay-off was emphatically smashed home by Gagliardini.
The midfielder then turned provider for Inter's third after being gifted possession by Lorenzo Montipo, with Lukaku only needing to sort his feet out before being left with a simple finish.
Montipo's opposite number Samir Handanovic made a similar error in passing straight to Caprari, who pulled one back for Benevento, but Hakimi stole in ahead of Luca Caldirola to restore Inter's three-goal cushion.
The home side should have conceded five in the first period but Arturo Vidal missed the target with a close-range header, and Benevento improved after the break, Gabriele Moncini hitting the post shortly after the restart.
Yet the woodwork denied Gagliardini too before a fifth and final Inter goal came courtesy of substitute Martinez 19 minutes from time.
Caprari at least made the final margin of defeat less severe with his second, but Inter could have had a six as Ivan Perisic somehow fired wide from Hakimi's cross and Christian Eriksen hit the bar.