Bayern defeated Barcelona as the German side, Sporting CP and Club Brugge all made it two wins from two in the Champions League's group stage.
Robert Lewandowski endured a disappointing return to his former club as Bayern struck twice in five second-half minutes to take control of Group C.
Liverpool's Joël Matip's 89th-minute header earned Liverpool victory and ended Ajax's seven-match winning run.
In the meantime, Club Brugge stunned Porto to start Group B with back-to-back wins.
Alsoe in Group B, Leverkusen gave Atlético a taste of their own medicine by scoring two late goals to collect their first points.
Edin Džeko scored one and set up another for Denzel Dumfries as Inter Milan made light work of Plzeň.
Sporting CP defeated Tottenham 2-0 as the Lions made it two wins from two after a remarkable finale in Lisbon, with the hosts scoring two late goals.
Marseille were defeated 1-0 in their clash against Frankfurt. Jesper Lindstrøm's first-half goal was enough to give the German side victory and consign Marseille to back-to-back Group D losses.
Captains will be the only ones allowed to speak to the referee and discuss a decision during matches at the upcoming European Championship in a bid to facilitate clearer communication.
Substitute Jhon Duran scored two late goals as Aston Villa fought back to salvage a 3-3 home draw with Liverpool on Monday and take a significant step towards a place in the Champions League next season.
Arsenal's Leandro Trossard capitalised on dreadful defending to secure a 1-0 win against Manchester United that saw the Gunners climb back to the top of the Premier League, ensuring the title race will be decided on the final day.
UAE Team Emirates rider Tadej Pogacar has retained his overall lead after Dutchman Olav Kooij won stage nine of the Giro d'Italia on Sunday, pipping Jonathan Milan by half a wheel right at the finish line in a breathless sprint at the end of a 214-km ride from Avezzano to Naples.