Frank Lampard’s side scored two own-goals and two penalties while Ajax had two players sent off on a chaotic night at Stamford Bridge.
Having trailed 4-1, the Blues battled back to level the scores and then Cesar Azpilicueta thought he had scored a winner, only for VAR to step in.
Nevertheless, a point from a breathless match keeps Chelsea firmly in the race to qualify from Group H.
Chelsea’s 1-0 win in Amsterdam last month had put them in control of the group but Ajax looked set to wrest it back following a lightning start.
Ajax fans were barred from attending following crowd trouble during their win over Valencia, although that did not stop hundreds from travelling to west London anyway.
The few that did make it in were celebrating inside two minutes, only to be silenced 60 seconds later in a breakneck opening.
Ziyech’s swirling free-kick flew over Kepa and hit the inside of the post, before smacking the Brazilian keeper full in the face and bouncing into the net.
It was a freakish goal but Ziyech’s delivery was superb, and for the third time in little more than half an hour Chelsea’s inability to defend crosses had cost them.
Things got even bleaker for the Blues 10 minutes into the second half. Ziyech found Donny Van de Beek in the area and the midfielder was given the time and space to turn and fizz a low shot past Kepa.
Chelsea reduced the deficit to two again when Pulisic’s cross was prodded towards goal by Abraham and Azpilicueta made sure at the far post.
Then in another crazy 60 seconds Daley Blind was shown a second yellow card for fouling Abraham and Joel Veltman followed him down the tunnel for handling Callum Hudson-Odoi’s shot.
Stamford Bridge was rocking as Jorginho rolled in his second penalty of the night, and it was pandemonium moments later when sub Reece James lashed home from a corner to equalise.
VAR then ruled out Azpilicueta’s dramatic late ‘winner’, spotting a handball among the pinball in the Ajax box, and visiting keeper Andre Onana denied Michy Batshuayi at the death as the Dutch champions held on.