Lyon, who won seven French titles in a row between 2002 and 2008 and made the Champions League semi-finals in 2010, took the lead thanks to Steed Malbranque on 25 minutes.
However, Nigerian Kehinde Fatai's goal after the break and a Constantin Budescu penalty nine minutes from time boosted Astra.
Lyon will still hope to turn the tie around in Romania next Thursday and qualify for the group stage of Europe's second tier club competition.
In other notable first-leg results, St Etienne were another French flop as they lost 1-0 at Kardemir Karabukspor to hand the Turks their maiden European victory while Moldova's Zimbru Chisinau surprised Greece's PAOK 1-0 at home.
Sweden's Markus Berg scored all four goals in Panathinaikos' 4-1 win in Greece over Danish league leaders FC Midtjylland while Legia Warsaw, thrown out of Champions League qualifying over an ineligible player, won 1-0 at Kazakhstan's Aktobe.
(Writing by Mark Meadows, editing by Pritha Sarkar)
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