Making just his fifth league start of the season, Christian Eriksen's seventh-minute free kick caused all kinds of problems, with Benevento defender Riccardo Improta getting the last touch as the ball found the net to break the deadlock.
Inter had a host of chances to make it 2-0 in the first half, but had to wait until the 57th minute for their second goal with Lautaro Martinez scoring for the first time in his last seven appearances in all competitions.
Martinez then turned provider for Lukaku, who fired home 10 minutes later to make sure of the win for Antonio Conte's side, before the Belgian took his Serie A tally to 14 for the season with another goal in the 78th minute.
The win took second-placed Inter onto 44 points and ensured they did not fall further behind leaders Milan, who beat Bologna earlier on Saturday, while maintaining a five-point gap to Juventus in third.
Filippo Inzaghi's Benevento stay 12th and are without a win in their last four league games.