The Ligue 1 outfit fell to a surprise 2-1 defeat on home soil last week, putting the Romanians firmly in the driving seat.
Steed Malbranque's 25th-minute opener gave Hubert Fournier's men an encouraging start, but Kehinde Fatai levelled for the visitors in the 72nd minute and Lindsay Rose received a costly second yellow card a few minutes later.
Constantin Budescu fired in a penalty in the final 10 minutes to earn a precious away win, but Astra coach Daniel Isaila knows the tie is not won just yet.
"We are really well prepared both physically and mentally," he said. "If you don't have self-confidence, it's impossible to achieve targets.
"Obviously the second leg will be very tough, because the mentality of the French players is to attack and to impose their game.
"But we have a psychological advantage and we will do our best."
Astra - bidding for a first appearance in the group stage of a continental competition - lost in this round to Maccabi Haifa last season, while Lyon made it to the quarter-finals.
Fellow French club Saint-Etienne host Karabukspor a goal down from the first leg, while Astra's compatriots Petrolul Ploiesti trail Dinamo Zagreb 3-1 ahead of their trip to Croatia.
Inter, who are - along with Juventus - the most successful team in Europe's secondary club competition, hold a sizeable 3-0 advantage over Icelandic minnows Stjarnan, but Serie A rivals Torino were held to a goalless draw by Split in their opening encounter.
Tottenham came from behind to get the better of AEL 2-1 in Cyprus and should be full of confidence following a 4-0 demolition of QPR in the Premier League but compatriots Hull City must overturn a 1-0 deficit against Lokeren of Belgium if their maiden European campaign is to go on.
There was success for the competition's Spanish clubs last Thursday.
Villarreal have one foot in the group stage after winning 3-0 at Astana, while Real Sociedad are a goal to the good against Krasnodar.
Borussia Monchengladbach will be hoping for a more straightforward home tie after beating Sarajevo 3-2 in the first leg, and Europa League involvement hangs in the balance for a trio of Dutch outfits.
Feyenoord, Twente and PEC Zwolle were held to first-leg draws by Zorya, Qarabag and Sparta Prague respectively last week.
PSV are a goal up against Shakhtyor ahead of the away leg.
Elsewhere, Apollon's match against Lokomotiv Moscow and Omonia Nicosia's tie with Dinamo Moscow are all square following draws in the first legs of the two Cyprus-versus-Russia encounters, while Swiss duo Young Boys and Zurich are 3-1 up in their respective fixtures with Debrecen and Spartak Trnava.
Metalist host Ruch Chorzow, Neftci are in action against Partizan, Zimbru travel to PAOK and Trabzonspor take a 2-0 advantage to Rostov.
Dnipro, Rijeka, Asteras Tripolis, Panathinaikos and HJK are all on the road against Hajduk Split, Sheriff, Maccabi Tel Aviv, Midtjylland and Rapid Vienna respectively.
In the round's remaining fixtures Nacional host Dinamo Minsk, Club Brugge are at home to Grasshopper, Aktobe head to Legia Warsaw, and Rio Ave welcome Elfsborg.
