Goals from Odsonne Edouard and Mohamed Elyounoussi saw Lennon’s side exact some retribution for their Champions League elimination at the hands of the Romanian champions back in August.
Celtic are now a point clear at the top of Group E, ahead of both Cluj and top seeds Lazio, who defeated Rennes 2-1.
Manager Lennon is still preaching caution when it comes to Celtic’s prospects of qualifying for the knockout stage of the tournament but is enthused by the potential of his squad.
“We are top of the group and it’s a great start,” he said. “It’s early, the group is still open, it’s tight. Cluj and Lazio both have three points and you can’t write Rennes off. Anyone can win this group. We have given ourselves a foothold in the group, that’s all.
“But the performances I’ve had in the first two games have given us a lot of food for thought in a positive way.
“We wanted a strong performance from the team tonight and I got more than that. I thought we were outstanding.
“My only disappointment is that we didn’t win the game by more. They are functioning as a team, there is a real solidity about us and fluidity going forward.
“We looked really strong and thoroughly deserved the win. There were some outstanding individual performances and from one to 11. I thought we were absolutely excellent against a very good side.
“I’m getting great performances from the team. I think there is more to come. I said to the players tonight that I think we have the makings of a good side. It’s embryonic in the season and I’m not getting carried away. But I’m absolutely thrilled and delighted for the supporters as well to have European football back here and a good performance from the team.”
Cluj manager Dan Petrescu, who had been confined to his Glasgow hotel room on the eve of the game because of illness, had no complaints about the outcome.
“We knew it would be very difficult to win here again,” said Petrescu. “Celtic are a very good side and now they know our ability to play football.
“Celtic have better players than us. I was very disappointed when we got them in the draw for this group. Celtic and Lazio are the big favourites. Normally, they should both go through. But we still have an opportunity.
“I felt very bad yesterday. I didn’t think I would make it to the game tonight. I was happy to be here but disappointed in the result.”