And he was showing plenty of appetite here even though he wasted a good chance for a second after the restart when he curled wide following more defensive errors from Augsburg.
Mignolet came to the rescue with 20 minutes to go after he came out to block Tobias Werner after he was allowed race through the Reds’ defence unmarked.
Liverpool avoided a late penalty when Alexander Esswein went down in the area under a challenge from Alberto Moreno before Stafylidis curled a free-kick just wide.
LIVERPOOL (4-3-3): Mignolet; Clyne, Lucas, Sakho, Moreno; Can, Henderson, Milner; Firmino, Sturridge (Origi 66), Coutinho (Teixeira 79).
Subs: Ward, Toure, Benteke, Smith, Chirivella.
AUGSBURG (4-2-3-1): Hitz; Verhaegh, Janker (Parker 90), Klavan, Stafylidis; Esswein, Altintop; Werner (Bobadilla 72), Koo (Moravek 80), Caiuby; Kohr.
Subs: Manninger, Opare, Max, Rieder.
Referee: Clement Turpin (France)