But first place in this Group F went to Borussia Dortmund who returned from a one-year absence in the elite event with a 6-0 triumph at Legia Warsaw. Mario Goetze, Sokratis and Marc Bartra put Dortmund 3-0 up after 17 minutes. Raphael Guerrero, Gonzalo Castro and Pierre-Emerick got the other goals.
Leicester had a dream start thanks to sloppy Brugge defending, with Albrighton tapping home in the fifth after defender Han Vanakan headed a long throw-in over the hands of his goalkeeper Ludovic Butelle.
Mahrez made it 2-0 just before the half-hour mark with a classy free-kick into the top left corner, and then also converted from the penalty spot in the 61st after Butelle brought down Jamie Vardy.
The Foxes top Group G ahead of Porto and Copenhagen who drew 1-1 with Hector Herrero scoring for the hosts and Andreas Cornelius for the Danes.
In Group C, City needed just eight minutes to go ahead against Gladbach, with Aguero slotting home Aleksander Kolarov's low cross at the near left post.
Aguero also made no mistake from the spot 20 minutes later - after missing two penalties in the play-offs - when he sent Yann Sommer the wrong way after Ilkay Guendogan was brought down.
He completed his hat-trick in the 77th, and Kelechi Iheanacho wrapped up matters as City drew level on three points with Guardiola's former club Barcelona who crushed Celtic 7-0 Tuesday.
Spurs opened their Group E campaign at Wembley - where they now play their home games in the event - and were two goals down against Monaco within half an hour from Bernardo Silva's long-range blast and Thomas Lemar.
Toby Anderweireld pulled one back with a header on the stroke of half-time but Spurs fought in vain for the equalizer, with Harry Kane wasting the best chance.
The other group game saw Leverkusen waste a 2-0 lead from Admir Mehmedi and Hakan Calhanoglu after 15 minutes in a 2-2 draw with CSKA Moscow, who rebounded from Alan Dzagoev in the 36th and Roman Eremenko two minutes later.
In Group H, ex-champions Juventus and Europa League winners Sevilla produced a goalless draw while Olympique Lyon are the first leaders from a 3-0 over Dinamo Zagreb from Corentin Tolisso, Jordan Ferri and Maxwell Cornet.