Chelsea started well and looked a constant threat throughout the game, taking an early lead through Alex Kiwomya who stabbed the ball past Peter Leeuwenburgh on 12 minutes.
Ajax responded almost immediately when Geordi Bitter headed in from close range after Danzel Gravenberch's shot had rebounded off the crossbar.
Despite the setback, the Blues looked in command of the game and the explosive Islam Feruz gave Chelsea the lead five minutes before the break with a cool finish.
After the restart, Chelsea continued to keep the ball well and Feruz doubled his tally on 49 minutes with a fine effort from 16-yards.
The Dutch side worked hard to get back into the game, and on 61 minutes were awarded a penalty which Lesley de Sa converted to make it 3-2 to the visitors.
The hosts pushed hard for an equaliser and were rewarded for their efforts in the last minute of the game, with Nick de Bondt firing in from close range to make it 3-3 at full-time.
The result means Chelsea progress through to the last 16 of the tournament alongside Ajax and CSKA Moscow from Group 3.
Last 16 ties:
PARIS ST GERMAIN v TOTTENHAM HOTSPUR
CSKA MOSCOW v PSV EINDHOVEN
SPORTING CP vLIVERPOOL
BARCELONA v CHELSEA
INTERNAZIONALE v ARSENAL
OLYMPIACOS v ANDERLECHT
JUVENTUS v ROSENBORG
AJAX v ASTON VILLA
