The Blues needed to avoid a heavy defeat to the Dutch outfit to ensure their passage to the next stage of the competition where, as one of the best third-placed sides, they will face Barcelona.
The hosts started the match strongly, forcing opposition goalkeeper Mitchell Beeney into a fine save from an early free-kick.
However, it was Dermot Drummy’s side who took the lead against the run of play, with winger Alex Kiwomya finding the back of the net after just 12 minutes.
Chelsea’s lead lasted all of just four minutes, though, as Jordi Bitter cancelled out the 16-year-old’s early goal.
The Blues quickly regained their composure and took charge of proceedings, with striker Islam Feruz particularly impressive.
The 17-year-old dispossessed Branco van den Boomen and darted into the area before cooly slotting the ball home five minutes before half-time to restore Chelsea’s lead.
Feruz added to his first-half goal almost immediately after the break, handing the visitors a two-goal advantage, and all but confirming the English side’s progression to the next phase.
The second half saw the weather quickly deteriorate, with strong winds and heavy rainfall affecting the quality of play on show, and Chelsea suffered.
Ajax, however, took full advantage when Alex Davey hauled down Lesley De Sa 15 inside the area 15 minutes from time. De Sa subsequently picked himself up to slot past Beeney, halving the deficit in the process.
The progressively worsening conditions made the game an unattractive struggle in the closing stages, and Chelsea were denied a famous victory in the Dutch capital - as well as second place in the group – as Nick de Bondt struck for Ajax to give his team a share of the spoils.