The Nerazzurri entered the contest knowing only three points would keep their hopes of progressing alive, and they did just that despite the match being too close for comfort at the end.
Matteo Darmian put the Italians ahead in the first half only for Alassane Plea to equalize in injury time. However Lukaku took over in the second half, bullying his way to two goals to seemingly put Inter on their way.
However Plea added a second and saw a third ruled out by VAR to the relief of Antonio Conte, as Inter held on long enough and will now fight for qualification on the final match day with Shakhtar.
Lautaro Martinez started strong and saw two chances come to nothing after a great Darmian cross, while Lukaku picked out Ashley Young with a cutback cross but his effort was deflected just wide of the mark
Inter’s strong start was rewarded in the 17th minute with a fine strike by Darmian. Roberto Gagliardini found the Italian with a great through ball down the right, and rather than crossing he fired between the goalkeeper’s legs to put the away side ahead.
Lautaro should have made it 2-0 when Lukaku started another dangerous counter and picked out the Argentine, however his first strike was blocked while Yann Sommer kept cool to palm away a dangerous strike from in close.
Stefan Lainer and Marcus Thuram tested Samir Handanovic as Gladbach slowly made their way back into the match before equalizing in stoppage time when Alassane Plea found himself unmarked in the six yard box and headed home Valentino Lazaro’s cross.
The blow of conceding late affected Inter early in the second half as Gladbach threatened on more than one occasion but were unable to make their efforts count.
Lautaro thought he had done enough to put Inter ahead after collecting a Lukaku layoff and leaving Sommer flatfooted with a great strike from distance, however the post had other plans.
There was no denying Inter minutes later as they took the lead thanks to some Lukaku brilliance. The striker bullied his way past Denis Zakaria and fired an angled strike with his right foot that found the far bottom corner.
Lukaku added to his tally soon after after Alexis Sanchez found Hakimi down the right, who rolled it through for the unmarked Belgian to fire home from 12 yards out.
However just when it seemed Inter would cruise to a priceless victory Sanchez gave the ball away in midfield, which allowed Plea to run through and pick out the far corner to make it 3-2.
The non-stop action continued at the other end when Sanchez cut into the are and pulled it back, hitting Lainer and falling for Young who couldn’t fire home from the goalline. It looked as though Inter had thrown it all away when Plea fired home from just inside the penalty area, however VAR called it back because Breel Embolo was offside and directly in the line of sight of the shot.
Nerves were high for both teams as the final minutes played out with Inter unwilling to keep possession despite being ahead, however the final whistle eventually came as the Nerazzurri picked up their first win of the competition in heart-stopping fashion.