Coupe de France: Red Star 2 Consolat Marseille 0
After a goalless first half in Friday's contest at the Stade de Paris, the hosts moved ahead when Allegro drilled home from a set-piece in the 51st minute.
Beziouen then made sure of the win from the penalty spot with four minutes left on the clock, after team-mate Naim Sliti had earlier missed from 12 yards.
Red Star, who sit third in the third tier of French football, had the better of the first half but were unable to find the breakthrough against their opponents, who occupy a spot in the relegation zone of the same divison.
It took just six minutes second-half minutes for the deadlock to be broken, though, as Allegro slammed home from the centre of the penalty area when the visitors failed to clear their lines from a corner.
Stili had the chance to double the lead with Red Star's first penalty, but his effort rebounded off the crossbar.
However, Red Star were awarded another spot-kick in the closing stages and Beziouen's effort squirmed under visiting goalkeeper Jean-Baptiste Geuydon, meaning Sebastien Robert's men can prepare for Ligue 1 side Saint-Etienne in the next round.