After defeats in their first two Group H fixtures to the Italians and Barcelona, a James Forrest penalty before the break and a deflected Beram Kayal drive early in the second half put the home side into a comfortable lead.
In the 88th minute Hoops substitute Nir Biton, who replaced Mikael Lustig, was shown a straight red card by referee Ivan Bebek for his challenge on Thulani Serero before Ajax substitute Lasse Schone grabbed an injury-time consolation.
With AC Milan drawing 1-1 at home to Barca, Celtic are within two points of the Italian club after three games with Ajax at the bottom of the table with one point ahead of the Hoops' trip to Holland in a fortnight.
The Celtic boss said: "It leaves us in a very good position.
"We will have to get a result in Amsterdam and that is going to be very difficult on tonight's evidence but it is not beyond us.
"We have three points, just two points behind Milan so the group is open for us again.
"It was a massive win in the context of the group.
"Ajax at home are a formidable side. They keep the ball well and kept possession.
"But credit to players, this our 19th competitive game so far.
"The squad is stretched. It was a heroic effort and I thought we thoroughly deserved to win the game."
Lennon, who insisted Kayal was "worth his weight in gold" for his goal and a saving tackle on Viktor Fischer in the first half, praised Forrest's bravery in taking the penalty when regular spot-kick taker Kris Commons was out through injury.
The former Celtic skipper said: "He keeps telling me he has never missed a penalty so this morning we had a chat and he said he would take it, because obviously Kris was out.
"He kept his cool because obviously there was a lot of gamesmanship going on from the goalkeeper but he kept his cool.
"It was a big moment in the game, just before half-time and it set us up very nicely for the second half.
On Biton's ordering off, Lennon said: "I had no complaints. He was late. I'm not convinced there was contact but he left a trailing leg."
"Although if he had been playing at Easter Road against Hibs on Saturday he would probably got a booking for that," added Lennon, alluding to his unhappiness at Hibs' tackling in the game that dominated the headlines.
Ajax boss Frank De Boer remains confident that his side can still get third place in the group.
The former Rangers player said: "Celtic didn't create anything although they scored twice, once with a penalty.
"We dominated the game but only scored once and should have equalised before they got their second.
"It is going to be very hard for us to get second place but I have confidence in the third place.
"We have one point and if we win at home we will be one point ahead of Celtic.
"It will be difficult but if we play that way again...eight times out of 10 the best team wins and I thought we were the best team.
"But only goals count and we will have to do it in the Arena."