In a first-ever European meeting between the two sides, it was the hosts who came close to an early breakthrough when Federico Dimarco’s powerful effort from the edge of the box drifted narrowly wide of the target.
That was a sign of things to come, as Inter looked to build on their early momentum, with Lautaro Martínez seeing a low strike thwarted by Péter Gulácsi in the Leipzig goal.
The Nerazzurri continued to dominate proceedings as the first half progressed and their pressure was duly rewarded in the 27th minute. A superb inswinging delivery from Dimarco caused confusion in the Leipzig box and Lukeba could only deflect the ball into his own net.
Having lost all four of their previous league phase matches, the visitors desperately tried to gain a foothold in the contest before half time, with their defence holding firm to keep the deficit down to just a single goal.
In a similar vein to the first half, Inter came flying out the blocks at the start of the second as Denzel Dumfries blazed over from close range and Hakan Çalhanoğlu saw a tame effort comfortably saved by Gulácsi.
However, for all the hosts’ pressure, the match remained tantalisingly poised heading into the final half-hour, with Leipzig threatening an equaliser against the run of play when Antonio Nusa’s curled strike was expertly parried away by Yann Sommer.
That near miss gave Marco Rose’s men plenty of encouragement late on, but despite their best efforts and a couple of half-chances, Inter held firm to secure a hard-earned three points.
The result extends the hosts’ unbeaten start to the league phase (W4, D1) as they move top of the standings while Leipzig’s miserable wait for a first point goes on.