Former Aberdeen player Duff, 35, spent a season with Astana's domestic rivals Kairat and knows the Kazakhstan Premier League well.
"It's very important that Celtic get a good lead, hopefully a couple of goals, at Parkhead," Duff told BBC Scotland.
"Astana is a very tricky place to play, Celtic found that out the last time."
The teams met in the third qualifying round last season, with the sides drawing 1-1 in Kazakhstan and Celtic winning 2-1 in Glasgow thanks to a late Moussa Dembele penalty.
Boss Brendan Rodgers believes Celtic's familiarity with Astana and previous trip to Kazakhstan will benefit them greatly this season.
Duff agrees and also believes the fact that the first leg is not until 16 August could also be crucial.
"Astana are very similar to last season - similar squad, same manager, similar danger players they had in the previous year," Duff explained.
"Astana have brought in a couple of Bosnians and a Hungarian player who have been doing very well for them in the league campaign.
"It's not the element of the unknown for Celtic as they've been there before, like Brendan Rodgers said. They know what they're going into.
"I'm confident that Celtic have got the attributes to hopefully win the game at Parkhead in the first leg, I think that's vitally important because it is a huge factor going over to Kazakhstan as they are very strong at home.
"They've had some very good home results in Europe - 3-1 against Legia Warsaw in the last round, and they are not a poor side at all.
"So I think it's very important that Celtic go there with a lead. It's very difficult playing on the 4G pitch over there and the atmosphere that the stadium creates.
"With it being a few weeks away, Celtic will have a couple more games under their belt and that will stand them in good stead. They will be up to match fitness and on their day,
"Celtic will be a match for any European team, at home or away - they're a very, very good side and I was so impressed with them last year.
"Astana are three quarters through their season, they will have the sharpness and touches. It should be an interesting tie but I have all faith in Celtic going through."
Stuart Duff believes Celtic will prove too strong for Astana in the Champions League play-off - but says it is vital the Scots take a lead to Kazakhstan.