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.
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