It was a must win for Celtic's qualification hopes as James Forrest opened the scoring from the penalty spot before a deflected goal in the second half off Stefano Denswil made it 2-0.
Celtic then had to hold off a ferocious Ajax onslaught - especially when Nir Biton was sent off for a dangerous tackle - but while Ajax did manage to claw one goal back in stoppage time, the Bhoys held on for a crucial three points.
"There was a lot of good fortune for Celtic - the breaks went there way and they scored the goals at good times," Collins toldSky Sports."Fraser Forster, as usual, came up with a great save at an important time, too.
"Ajax are a great football side, they created chances but their strikers never finished them off. Celtic kept going, stuck together and defended well when they got their noses in front. That is a massive three points."
On Biton's red card, Collins added: "I thought the referee was lenient all night but these tackles when you go to ground and lift your studs off the ground are dangerous - he hardly touched the guy but the referee has seen it as dangerous play.
"There was no need for him to go to ground, he should have stayed on his feet and he left his team with a lot to do in the last 10 minutes."
The win gives Celtic a foothold in the group after losses to AC Milan and Barcelona, but Collins says they will be up against it again when they head to Amsterdam.
"It is going to be a real test in a fortnight when Celtic go to Ajax," he said.
"They are a good football team, well organised and they play the Barcelona way - passing and moving the ball all night long - so they have great patience.
"They could have scored more goals tonight [Tuesday] so it is going to be tough for Celtic who will be going there with key players missing.
"However Celtic proved that they are resilient; they keep going and stuck together with a terrific team spirit.
"They will go to Amsterdam with hope."