Ajax were 4-2 up at Stamford Bridge in the Group H clash when Daley Blind fouled Tammy Abraham.
Referee Gianluca Rocchi allowed play to continue, and Callum Hudson-Odoi's subsequent shot hit Joel Veltman's arm in the penalty box.
Rocchi pointed to the spot and then duly issued Blind and Veltman their second yellow cards, reducing Ajax to nine men.
Jorginho scored from the spot for the second time in the game to make it 4-3 with 19 minutes remaining, and Reece James equalised on 74 minutes before the video assistant referee ruled out Cesar Azpilicueta's winner:
In the madness, Pulisic said he did not notice two of Ajax's players had seen red despite being in the thick of the action, per MailOnline's James Dutton: "[The penalty] made the game even wilder and gave us more confidence to get those next two goals. The whole thing was crazy, I didn't even realise they got two red cards to be honest. It was pretty wild."
Pulisic, 21, joined Chelsea in the summer after signing for the Blues back in January and going back to Borussia Dortmund on loan for the remainder of the 2018-19 campaign.
He was initially used only sparingly by manager Frank Lampard, but he has flourished recently with four goals in four consecutive starts:
Chelsea's comeback from 4-1 down to claim a point against Ajax could be crucial to their ambitions of qualifying for the 2019-20 knockout stages.
After Valencia's 4-1 win over Lille on Tuesday, Group H is now the most tantalisingly poised in the tournament:
The Blues visit the Mestalla on November 27 to face Los Che, which could end up being the deciding game for which side qualifies out the group. The Premier League side then finish their group-stage campaign with a home clash against Lille on December 10, which they will expect to win.