The victory at the Marin Anastasovici Stadium in Giurgiu, a town on the banks of the Danube, stretched Astra's lead over second-placed Steaua to six points with three games remaining.
Centre back Valerica Gaman slotted home a penalty on the stroke of halftime after Denis Alibec was brought down by Steaua keeper Florin Nita.
Alibec calmly made it 2-0 in the 77th minute thanks to another penalty after substitute Filipe Teixeira was fouled in the penalty area by Fernando Varela.
Under coach Marius Sumudica, Astra are taking the fight to Steaua, who have won the title for the last three seasons.
"It’s just a feeling of immense joy but we still need to get four points in the next three matches," Sumudica told reporters.
After the match, flamboyant Steaua owner Gici Becali said he was going to quit the 26-times Romanian champions.
"I'm quitting football, I'm done with that," Becali told reporters. "I don't want to be here anymore."
(Reporting by Angel Krasimirov; Editing by Toby Davis)
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