Holders Real Madrid were two minutes from losing at home to Sporting Lisbon in their opening group game before staging a late comeback to win 2-1.
Bruno Cesar's second-half goal looked to have given the Portuguese side a memorable triumph at The Bernabeu, yet ex-Sporting forward Cristiano Ronaldo popped up with a late leveller before Alvaro Morata snatched a winner four minutes into stoppage time.
Borussia Dortmund had no troubles elsewhere in Group C as they recorded a 6-0 demolition of Dundalk’s conquerors Legia Warsaw.
Mario Gotze, Sokratis Papastathopoulos and Marc Bartra all scored in the opening 18 minutes and Raphael Guerreiro, Gonzalo Castro and Pierre-Emerick Aubameyang added more goals after half-time.
Leicester made a dream start in their first ever Champions League game by defeating Club Brugge 3-0 in Belgium, but Tottenham suffered a dose of Wembley woe against Monaco.
Claudio Ranieri's Foxes, last season's unlikely Premier League title winners, had lost both of their opening away games domestically but had no such trouble on the continent.
Marc Albrighton broke the deadlock for Leicester before two set-pieces from Riyad Mahrez either side of half-time, one free-kick and the other a penalty, ensured the club's historic night will be remembered fondly.
It was a landmark night for Spurs too as they broke an English club home attendance with 85,011 watching at Wembley, yet the majority were left disappointed as Monaco emerged with a 2-1 win.
Bernardo Silva and substitute Thomas Lemar had put the French side two goals up in a venue which provided mixed results for Arsenal when they, like Tottenham, used it as their temporary home in the late 1990s.
Toby Alderweireld headed in an Erik Lamela corner prior to the break but Mauricio Pochettino's side were unable to muster a leveller.
Sergio Aguero put his domestic suspension to one side to grab a hat-trick as Manchester City defeated Borussia Monchengladbach 4-0 in their rearranged clash.
Having seen the contest postponed on Tuesday night due to heavy rain in the north-west, Aguero opened the scoring with a near-post finish before converting a penalty to make it 2-0 prior to half-time.
And, though he will sit out the next two domestic fixtures due to a ban triggered after his elbow on West Ham's Winston Reid, the Argentinian showed his value to City in this competition by completing his hat-trick. He was then substituted and his replacement Kelechi Iheanacho added a stoppage-time fourth.
Juventus were held to a 0-0 draw by three-time Europa League winners Sevilla in Italy, while Porto and Copenhagen also shared the spoils having drawn 1-1, with ex-Cardiff striker Andreas Cornelius scoring for the visitors.
Bayer Leverkusen, who led 2-0 after 15 minutes, could only draw 2-2 at home with CSKA Moscow in Tottenham's group but Lyon had no such issues at home, recording a comfortable 3-0 success over Dinamo Zagreb.