The Eagles, looking to capitalise on Sporting Lisbon's draw at home to Pacos De Ferreira and Porto's away defeat against Nacional, got off to the worst possible start when Roberto fired a shot past Julio Cesar in the third minute.
Benfica tried to pull themselves back on level terms before the break. However, despite the visitors enjoying 74% possession and having 15 shots at goal in the opening 45 minutes alone, Arouca were able to stay in front at the interval.
They nearly fell further behind when Nuno Valente took aim at the visitors' goal only to be denied by Cesar.
Midway through the second half, Andrade's introduction almost paid off after his strike from distance was close to finding a way through Rafael Bracalli.
However, Arouca were able to hold on to their slender advantage and are the only team in Portugal's top flight to still have a perfect record.