Real Madrid needed two late goals to beat Leipzig as boss Carlo Ancelotti became the second manager to win 100 Champions League games.
Leipzig missed a host of good chances with Christopher Nkunku denied by Thibaut Courtois twice.
Federico Valverde gave Real an 80th-minute lead from Vinicius Jr’s pass.
And Marco Asensio scored an excellent first-time finish from the edge of the box from Toni Kroos’ free-kick to seal the win for the European champions.
This is the first time they have won their opening two Champions League games since 2017-18.
Only Manchester United legend Alex Ferguson (102) has won more games in the tournament than Real boss Ancelotti.
Source: BBC Sports