Bayern made the best possible start with Mats Hummels heading in a cross from Arjen Robben after only four minutes.
Having never lost at home in any four previous clashes with Ajax in Europe, the Bavarians were on course to keep their record intact.
But the Dutch took back the ascendancy and with their bits of possession pressed forward with Nicola Tagliafico being sent through to pick out Dusan Tadic with a cross, but the Serbian missed.
The leveller finally happened as Noussair Mazraoui played a nice one-two with Tadic to guide a delicious finish beyond the reach of Manuel Neuer on 22 minutes.
Bayern finally woke up as Franck Ribery made a darting run down the right to play a low cross but Robert Lewandowski’s late reaction saw him miss out on the chance to add on the tally.
Just after the half and hour mark, Javier Martinez picked up a loose ball from just outside the box and fired a 30-yard drive that missed the intended target.
The game appeared to have swung in Bayern’s favour once again, with the Amsterdam club finding little space to manufacture anything out of the ordinary.
There was to be a scary moment for the five-time champions as Hakim Ziyech was inches close from handing them the lead with a well-taken strike just before halftime.
After a good start to the second half, Ziyech and David Neres combined to play in Tadic who scuffed the attempt.
Another great opportunity fell to Ajax but a good save by Neuer kept out Tagliafico from handing them the lead.
The Bavarians got out of their shelve after a threatening strike from range by Thiago Alcantara brushed the outside pole closer on 67 minutes.
Ajax missed another chance to go in front when Donny van de Beek missed a good chance with a header after a good delivery from Daley Blind.
Colombian James Rodriguez aimed to take matters in his own hands and launched at Andrey Onana who kept out the effort with a good save on 77 minutes.
In added time, A marvellous free-kick from Lass Schone found the top of the crossbar, leaving Ajax to rue their missed chances to go ahead in the group.
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