In a tightly contested tie, Nicolo Barella’s downward header stunned the Portuguese league leaders and gave Inter a priceless advantage.
Benfica struggled to dictate play in front of their own fans as Inter produced a defensive masterclass in Lisbon.
Rafa Silva was denied by Andre Onana’s first-half save before Inter’s Netherlands defender Denzel Dumfries produced a crucial block from close range as Benfica pushed for an equaliser.
The Italian visitors wrapped up a solid win when substitute Lukaku, on loan from Chelsea, scored from the spot after former Inter player Joao Mario handled inside the box.
Premier League referee Michael Oliver awarded the penalty after watching a replay of the incident on the pitchside monitor, with replays showing the ball struck the side of Mario’s head before hitting his hand.
Simone Inzaghi’s side will fancy their chances of finishing the job in front of their own fans in the return leg on 19 April.