The point was enough to put Bayern into the last 16 as group winners on a bad-tempered night in Amsterdam with five goals, two penalties and two red cards in an action-packed second half.
"That was an advert for football," beamed Bayern head coach Niko Kovac.
"We had the clearer chances and could have finished the game much sooner, but we didn't use the spaces.
"However, the most important thing was to finish top of the group and with 14 from 18 points we are happy."
Kingsley Coman came off the bench to put Bayern 3-2 up on 90 minutes before Nicolas Tagliafico equalised for Ajax in the fifth minute of added time.
After Lewandowski gave Bayern a first-half lead, Ajax turned the game around after the break as Dusan Tadic tapped home, then converted a penalty with eight minutes left.
However, Bayern roared back with Lewandowski scoring a spot-kick three minutes from time before Coman put the Germans back in front and Tagliafico could only rescue a point when victory would have seen the Dutch outfit usurp their opponents at the top of the table.
Lewandowski's brace leaves him as the Champions League's top-scorer with eight goals in the group stage.
- Dangerous challenges -
Ajax's Maximilian Woeber and Bayern forward Thomas Mueller were shown straight red cards for dangerous challenges.
There was little hint of the drama to come when Bayern took the lead in only the 13th minute at Ajax's Johan Cruyff Arena when Serge Gnabry's perfectly-timed pass put Lewandowski in behind the Dutch defence.
It should have been 2-0 14 minutes later when Gnabry served up a great chance for Lewandowski, but a fantastic save by Ajax goalkeeper Andre Onana blocked his shot.
Having earned a 1-1 draw in Munich at the start of October, Ajax kept the Germans under pressure.
It was 1-0 to Bayern at the break, but the Germans found themselves in the unusual position of enjoying just 40 percent possession, content to sit back and hit Ajax on the break.
Bayern were under intense pressure and the hosts deservedly drew level after a series of high-speed passes opened the away defence, giving Tadic a simple tap-in at the far post with an hour gone.
The game sparked into life with Onana again producing another superb save to deny Lewandowski moments later, just before Woeber was sent off for lunging in on Goretzka's ankle.
Mueller trudged off soon after, leaving Tagliafico with a bloodied head with 15 minutes left for going in high on the Argentinian.
Mueller's red card swung the momentum back in Ajax's favour.
Jerome Boateng's clumsy foul on Danish substitute Kasper Dolberg gave Ajax a penalty which Tadic slammed home.
Substitute Thiago Alcantara won the penalty Lewandowski slotted in and Coman's superb curling shot made it 3-2, before Tagliafico gave Ajax short-lived hope.