The Spaniard powered domestic a sweet left-footed strike five mins from time at the Red Bull Arena to breach Rangers' cussed defence.
Leipzig had struggled to break the impasse as Rangers limited them to simply 10 shots notwithstanding boasting 70 percent ownership.
The Germans can be seeking to attain their first European final - in Seville on May 18th against both Eintracht Frankfurt or West Ham - in subsequent Thursday's return game in Glasgow.
However, this turned into a beneath-par show from the hosts, who had a fifteen-game unbeaten run ended closing Saturday after they conceded two overdue goals at domestic to Union Berlin in the Bundesliga.
Leipzig teach Domenico Tedesco began with a three-guy attack of Dani Olmo, Dominik Szoboszlai and Christopher Nkunku, with each Andre Silva and Yussuf Poulsen left at the bench.
Rangers' lower back four sucked up everything the Leipzig assault threw at them early on, with Gers captain James Tavernier throwing himself into endless tackles.
A region of an hour had exceeded before the hosts created the first clear threat, but Nkunku couldn't get his shot away.
Both teams had opportunities early inside the second half of. Ryan Kent fired simply wide after dribbling into the location, then Tavernier had a shot charged down for the traffic.
Rangers goalkeeper Allan McGregor became forty in January, however he confirmed tremendous reactions to dam a effective shot from Nkunku, who later fired huge with the goal at his mercy.
