Celtic 0 Ajax 1 (Agg 3-2)
Martin O'Neill has led Celtic to the Champions League group stages for the first time in the club's history.
However Ajax did everything in their power to scare a nervous home support and gatecrash their party.
A magical first-half goal from Wambert Campos gave the Dutch side hope of pulling off a sensational comeback.
Celtic knew that the Dutch side would throw everything at them after their disaster in the Amsterdam Arena a fortnight ago and O'Neill found two heroes tonight in Johan Mjallby and Joos Valgaeren.
The defensive duo passed late fitness tests to play and were both instrumental in an almost flawless defensive performance.
Celtic started the brighter of the two sides and should have completely killed the tie off after just one minute.
Johan Mjallby got away from his marker at the back post to head Steve Guppy's floated free-kick across the face of goal but Joos Valgaerenfailed to finish from close range.
Ajax looked vulnerable from crosses in the early exchanges and Henrik Larsson found space in the area moments later to head Guppy's inswinging cross just over the bar.
The expected onslaught from the visitors did not materialise, but Shota Arveladze, scorer in Amsterdam, gave Celtic a warning in the sixth minute with a flashing long-range shot just past the upright.
Celtic's task should have been made easier in the 16th minute when Larsson, in full flight, was brutally hacked down by Abuhakari Yakubu near the touch line.
The home fans were vying to see red, but Italian referee Stefano Braschi brandished a yellow card instead.
Douglas was called to the rescue in the 20th minute from going a goal down, as his defence stood still.
Campos' attempted chip into the box came off the head of a Celtic player and into his path, but Douglas was quick off his line to deflect his effort wide of the post.
But the visitors were now enjoying a fair amount of possession and were causing the home side all kinds of problems on the break.
When the lively Campos played the ball up to Arveladze and skillfully dragged the ball back into his path to send him clean through to slot the ball past Douglas, a nervous hush fell over Parkhead.
Celtic were clearly rattled and again had Douglas to thank two minutes later as Arveladze got away down the left and unleashed a fierce left-foot shot which the keeper could only punch away.
Ajax still needed to score two more goals in the next 45 minutes and to stop Celtic from scoring to go through.
Celtic had to dig deep to stop the flow and their nervous supporters were doing their utmost to spur them on.
Ajax coach Adriaanse tried to freshen his side up in the 66th minute by replacing Nikos Machlas with Zlatan Ibrahimovic, but despite looking dead on their feet Mjallby and Valgaeren appeared to be holding out.
O'Neill was looking to kill off the match and he decided to bring on playmaker Lubo Moravcik for McNamara in the 72nd minute while Richard Knopper replaced Ferdi Vierklau for Ajax.
A flare among the Ajax fans was causing concern and police clashed with a small number of Dutch fans.
But nothing could ruin the celebrations at the final whistle as the European Cup winners of 1967 and manager O'Neill look forward to joining football's elite again in tomorrow's draw. -PA