Harry Kane claimed with a hat-trick of penalties in a four-goal haul as Bayern Munich demolished Dinamo Zagreb 9-2.
The England captain equalled Wayne Rooney's record of 30 goals in the competition - the most by an English player - when he converted a 19th-minute spot-kick, and then went past him with a 57th-minute finish before extending his record.
In the meantime, Raphael Guerreiro and Michael Olise looked to have put the hosts in complete charge by half-time at the Allianz Arena, but Bruno Petkovic and Takuya Ogiwara dragged Dinamo right back into it at 3-2.
However, Kane and Olise each struck for a second time within three minutes of each other and then the former Tottenham frontman completed his quadruple with two more penalties before substitutes Leroy Sane and Leon Goretzka completed the rout.
Reigning champions Real Madrid needed late goals from Antonio Rudiger and substitute Endrick to finally break Stuttgart's stubborn resistance.
After a goalless first half, Kylian Mbappe had put the home side ahead but Deniz Undav's equaliser kept the Germans in it until seven minutes from time - when Rudiger and then Endrick intervened to seal a 3-1 win.
Central defenders Ibrahima Konate and Virgil van Dijk both scored as Liverpool came from behind to win 3-1 at AC Milan.
Aston Villa paid the perfect tribute to former striker Gary Shaw as they enjoyed a dream start to their campaign with a 3-0 win at Young Boys.
Kenan Yildiz, Weston McKennie and Nicolas Gonzalez were on target as Juventus powered their way to a 3-1 home victory over PSV Eindhoven.
Yildiz and McKennie had the hosts 2-0 up by the break and when Gonzalez struck seven minutes into the second half, the points were safe despite substitute Ismael Saibari's stoppage-time
Champions League
soccer
Sport
Wayne Rooney
Michael Olise
Kylian Mbappe
Virgil Van-Dijk
Antonio Rudiger
Weston Mackennie
Deniz Undav
Leon Goretzka
Nicolas Gonzalez
Raphael Guerreiro
Ibrahima Konate
Kenan Yildiz
Bruno Petkovic