The 19-year-old Frenchman, in his second season at the club, scored acrobatically from a rebound after Augsburg goalkeeper Marwin Hitz parried Yussuf Poulsen's header.
Midfielder Naby Keita capped an inspirational display by scoring the second with a deflected free-kick in the 70th minute, the Guinea international's fourth league goal of the season -- all of them from outside the area.
Leipzig dominated the game although goalkeeper Peter Gulacsi made a difficult save from Daniel Baier's shot just before the second goal.
Kevin Kampl was close to a third for Leipzig when he struck the crossbar from a free-kick and Timo Werner nearly put away the rebound.
Leipzig are second in the Bundesliga with 38 points, three ahead of Bayer Leverkusen, who host Hertha Berlin on Saturday afternoon (Sunday morning AEDT) when runaway leaders Bayern Munich (53 points) host Schalke.