Goals from James Forrest and Beram Kayal gave Celtic a 2-1 win, which they desperately needed to make their last 16 aspirations look credible.
Neil Lennon felt quite a weight around this fixture, with suspension and injury robbing him of key players. But once again the Celtic manager came good on the European stage.
The thought lingers that Lennon's Celtic had played bravely and astutely prior to imploding in the last eight minutes against Milan in Italy five weeks ago. Clearly, Lennon does not quake in this elite setting, as Ajax were the latest to discover.
With Milan and Barcelona drawing 1-1 in Italy, Group H now has a competitive look about it, with Celtic up and running, and looking in contention in third place.
This was no mean feat for Lennon and Celtic in beating the Dutch champions, who showed plenty evidence of the quality they possess. Ajax struck a post and forced Fraser Forster into two crucial saves before allowing Celtic to slip their grasp. In the dying seconds Lasse Schone struck an Ajax consolation goal.
Lennon savoured the win, as he had come through another minor storm. Group H, packed with prestigious opponents, has looked unforgiving for Celtic, but Lennon exhibits a clear head on these European nights.
The Celtic manager had his work cut out in prising these three points. Scott Brown continues to divide opinion, but the Celtic captain's suspension, on top of other matters, left Lennon facing some acute decision-making over his midfield.
With Brown out, and Kris Commons and Adam Matthews injured, Celtic were denied three of their best players. But Lennon's decision to pair Kayal with Charlie Mulgrew in midfield, while relegating Joe Ledley to the bench, was vindicated by events.
Kayal has infuriated many Celtic supporters with his indifferent form, but he was a significant player against Ajax, making timely interventions, let alone scoring his first goal in two and a half years.
Fortune favoured Celtic, there can be no argument. Ajax had arguably been the better team prior to falling behind, and then watched as Forster blocked from Thulani Serero before Kayal struck a second for Celtic after 53 minutes.
All this was thrilling to behold from Celtic, though their Dutch visitors must have been mystified by their adversity. Ajax gave plenty to this game and must have felt a mite unlucky.
Forrest, a near rarity in Celtic's line-up as a prized, homegrown talent, gave Celtic the lead two minutes before the interval from the penalty spot. Ajax up to this point, arguably, had looked the more threatening team.
When Stefano Denswil upended Anthony Stokes, Forrest was made to wait while yellow cards were issued, and Jasper Cillessen, the Ajax goalkeeper, aimlessly strolled around his six-yard area as a distraction. But Forrest then calmly slotted the penalty passed the goalkeeper.
In the immediate wake of Forrest's goal the visiting Ajax fans were seen to rip out Celtic Park seats and hurl them around, as police and stewards waded in among the visiting supporters.
Having quoted Celtic's list of missing players, Ajax were also minus four players - Niklas Moisander, Bojan Krkic, Ruben Ligeon and Lerin Duarte - all of whom might have featured in Frank de Boer's starting XI. The truth is, barring a multitude of missing men, squad-strength in the Champions League should suffice.
This victory for Celtic also provided a reminder of that other Champions League spin-off…the ringing cash-till.
The value of the tournament remains vital to the Scottish champions. Last season, counting all its revenue streams, Celtic accrued over £22 million from the competition. It cannot be over-estimated.
The one blot for Celtic was a straight red card shown to substitute Nir Biton for a high tackle three minutes from time.
Victory, though, proved a balm for any other minor Celtic irritations.