A frantic start in west London saw Tammy Abraham score an own-goal and Jorginho level from the penalty spot inside the opening five minutes.
Quincy Promes had a hand in forcing Ajax's first, but the Dutchman was well-placed to make it 2-1. Hakim Ziyech then forced a second own-goal off Chelsea goalkeeper Kepa Arrizabalaga from a ridiculous free-kick to make it 3-1 before the break.
Donny van de Beek resumed the scoring after the break and netted an easy fourth for Ajax before Chelsea captain Cesar Azpilicueta pulled a second back at the far post.
Ajax then had both central defenders, Daley Blind and Joel Veltman, sent off for two yellow cards apiece in a sequence that ended with Jorginho converting his second penalty to make it 4-3.
Substitute Reece James hauled Chelsea level when he tucked a rebound into a nearly open goal, and Azpilicueta was unlucky to have a second ruled out by the VAR as the two teams shared the spoils.
The first half was an exhibition from set-piece situations, with Chelsea looking particularly vulnerable from the dead ball while Ajax appeared capable of scoring at just about every turn.
Abraham couldn't adjust his body in time to prevent Promes' cross angling in after less than two minutes, but Christian Pulisic continued an improved run of form and won a penalty shortly after.
Jorginho displayed his characteristic run-up and got the better of goalkeeper Andre Onana to equalise (U.S. viewers only):
The first half looked as though it was an exercise for Ziyech, however, and the attacking midfielder continued to show why it's he who is attracting the most transfer talk from this current Ajax crop.
He got the first of three assists on the evening with his pinpoint cross into Promes, who was assured from short range (U.S. only):
Squawka showed how it had been a frustrating first 20 minutes for the Netherlands winger:
It's not often own goals can be described as beautiful, but Ziyech showed that even the unintentional can look effortless with his free-kick from an acute angle on the 35-minute mark. Kepa was caught off guard by Ziyech's effort from near the corner flag, and the ball flew into the net via his face after the Moroccan's sensational set piece crashed back off the far post (U.S. only):
Kurt Zouma almost gave Chelsea their dream start to the second half, slaloming from defence and deep into Ajax territory, showcasing several step-overs before he flashed a wild attempt over the crossbar.
Azpilicueta moved to left-back when James came on for Marcos Alonso at the break, with Frank Lampard hoping to mute the creative genius of Ziyech on that side of the field.
Stamford Bridge spirits appeared to be on the rise, but Chelsea were sucker-punched just as momentum was climbing when Van de Beek found space to convert an easy fourth.
David Neres zipped down Ajax's right flank before Ziyech took over inside the Chelsea box, steering his pass inside for Van de Beek to score with his second touch.
Again, Chelsea responded in quick fashion when Azpilicueta got the last touch at the back post (U.S. only):
Chaos unfolded minutes later, beginning with a clumsy challenge from Blind that earned him a second yellow. Chelsea played the advantage in the same phase and Veltman was also sent off after he was controversially adjudged to have handled the ball in the area (U.S. only):
Jorginho again converted the resulting spot-kick, and barely three minutes had passed before substitute James made his effort count from the middle of the box (U.S. only):
The full-back's goal also meant he became Chelsea's youngest goalscorer in Europe's first-tier competition, per Sky Sports Statto:
Azpilicueta had his second and a potential Chelsea winner in the back of the net, but whereas his first just about squeezed past a check from VAR, this one was pulled back for hand ball.
Lampard looked incredulous after the fourth official signalled for only four minutes of second-half injury time, presumably wondering where the additional time from the other stoppages had gone.
But Erik ten Hag's alterations proved sufficient as his team fought to take an ultimately valuable point from the fixture, a far cry from what they expected at 4-1 up in the 55th minute.
Goal's Nizaar Kinsella described mixed scenes at half-time, though Lampard showed great sportsmanship to lead a peaceful union:
It's difficult to judge whether Chelsea will be happier with the point after falling three goals behind, or Ajax having lost two men away from home. However, the Blues will crucially keep the superior head-to-head record following their 1-0 win in Amsterdam.
Chelsea are at home again on Saturday when they host Crystal Palace in the Premier League, whereas Ajax return to Eredivisie action on Sunday at home to Utrecht.