Defender Yuri Logvinenko headed the home side ahead from a corner in the 19th minute at the noisy Astana Arena and the Hoops had to withstand some heavy pressure.
However, in the 78th minute, striker Leigh Griffiths drilled in a shot from the edge of the box to stun the Kazakhstan champions, a fightback that pleased the former Liverpool manager no end ahead of the second leg next week.
Rodgers said: “It was an outstanding result for us. Collectively the mentality was the most pleasing thing.
“I thought Eoghan was outstanding as a young player coming into that environment. I’m proud of him and the young players.
“I was disappointed with the goal, it is nothing new, but we showed a wonderful mentality to keep fighting and, in the second half, we restricted them to not so many clear chances and ended up scoring a fantastic goal.”
With five central defenders either out injured or catching up on fitness, the former Liverpool boss gambled by giving a European debut to 20-year-old O’Connell, who spent the early part of the summer on loan at Cork City. The Irish defender was put alongside the often-criticised Ambrose, with Mikael Lustig and Kieran Tierney either side as full backs, though there was fluidity in the system.
A midfield of Patrick Roberts, Callum McGregor, Scott Brown, and Stuart Armstrong was given a licence to support strikers Griffiths and Moussa Dembele.
Amid a promising start for the Hoops, it was Griffiths who had an effort on the turn from 20 yards which trundled wide. By that time O’Connell had flattened home forward Patrick Twumasi and then gave possession away 30 yards from goal, but at no cost.
However, there was a price to be paid when Ambrose allowed a cross from Twumasi to go through his legs, with Lustig having to concede a corner and, when Twumasi’s set-piece came in, Logvinenko got in front of keeper Craig Gordon to head in, with O’Connell also culpable.
After Dembele went down in the Astana box under pressure by Igor Shitov — penalty claims were ignored by Italian referee Paolo Mazzoleni — the Hoops’ goal had to survive a couple of more dangerous corners. In the 52nd minute, Nurgaliyev clipped the top of the bar with a drive after Abzal Beysebekov had got past Tierney all too easily.
Midfielder Nir Bitton replaced Dembele just after the hour mark to leave Griffiths foraging alone, but still Astana looked menacing.
However, the Hoops equalised, as Roberts won the ball from Dmitri Shomko and set up Griffiths to rifle his shot past keeper Nenad Eric for what could be a crucial goal.
In a frantic finale, Gordon saved from Kabananga with his foot, but in the five added minutes, Celtic were equally threatening.
Eric; Shitov, Logvinenko, Anicic, Shomko; Maksimovic, Canas; Beysebekov (Ibraimi 85), Nurgaliyev (Muzhikov 62), Twumasi; Kabananga (Despotovic 86).
Mokin, Tagybergen, Najaryan, Maliy
Gordon; Lustig, Ambrose, O’Connell Tierney; Roberts, Brown, McGregor (Rogic 77), Armstrong (Forrest 72); Dembele (Bitton 62), Griffiths.
Fasan, Janko, Izaguirre, Ciftci
Paolo Mazzoleni (Bergamo).