The result means that Inter still have a chance to qualify for the last-16 after Real Madrid’s shock loss against Shakhtar Donetsk.
The Italian side who went into the game without a win in any of their opening Group B games were ahead in the 17th minute after Matteo Darmian beat Yann Sommer to score his first goal for the club.
The hosts were level just before the break with a goal from Alexander Plea. The Frenchman who was left unmarked at the back post was able to cushion a header downwards past Handanovic to level the scores after being found by Lazaro.
Gladbach would have qualified as group leaders had result remained that way, but Inter as Lukaku had other ideas.
The Belgian restored Inter’s lead 20 minutes after the break with a right-footed effort after bullying his way past Zakaria. The striker was then on hand to convert this second for the night and Inter’s third following a nice run by Hakimi.
Alexander Plea scored his second for the night in the 75th minute, but it was not enough to deny Inter a big win for the night.
The result means that Inter now have a chance of qualifying for the knock-out stages when they play Shakhter Donetsk next week with a win for them and a loss for Real Madrid enough to hand them a spot in the last 16.