Liverpool have gone top of Champions League Group E after edging Genk 2-1 at Anfield.
The Reds had beaten the Belgians away last time out and repeated it again at home.
Georginio Wijnaldum gave Jurgen Klopp's side a 14th minute lead, before Mbwana Samatta headed in an equaliser just before half-time.
However, Champions League holders Liverpool got their winner on 53 minutes through Alex Oxlade-Chamberlain.
The win puts Liverpool a point clear of Napoli. Carlo Ancelotti's side drew 1-1 at home to Red Bull Salzburg.
There was more drama at Stamford Bridge though. Ajax took a 2nd-minute lead through Tammy Abraham's own goal. But Chelsea leveled just two minutes later thanks to a Jorginho penalty.
However, Ajax then raced into a 4-1 lead by the hour mark. Quincy Promes made it 2-1 on 20 minutes, before Kepa Arrizabalaga deflected in Hakim Ziyech's free-kick.
The home side suffered another blow when Donny van de Beek scored Ajax's fourth on 55 minutes. But the game would quickly turn on its head. Cesar Azpilicueta pulled one back for Frank Lampard's side.
Then two second yellow cards for Dutch pair Daley Blind and Joel Veltman saw Ajax reduced to nine-men with just over 20 minutes to go. Jorginho scored another penalty for Chelsea with 19 minutes to go and Reece James then made it 4-4 just three minutes later.
Chelsea thought they'd won it through Azpilicueta but VAR ruled the goal out. That eight-goal thriller levels both sides level on seven points in Group H. Valencia joined them on seven after thrashing Lille 4-1.
Elsewhere, Slavia Prague held Barcelona to a 0-0 draw at the Nou Camp. In the other Group F game, Borussia Dortmund saw off Inter Milan 3-2 to move up to second in the group, just a point behind Barca.
In Group G, RB Leipzig rose to the top after winning 2-0 at Zenit St Petersburg. Lyon go up to second after a 3-1 win at home to traditional giants Benfica.