The visitors have now lost three out of their last four games, with Stroppa choosing now as the right moment to depart.
Siena coach Serse Cosmi labelled the game as "tricky," "important" as well as "fundamental" and knew defeat would leave him close to the axe.
Both sides were hampered by injuries. The home side were without Reginaldo, Ze Eduardo and Massimo Paci, but welcomed back Alessandro Rosina. The depleted Delfini made the trip without top scorer Vladimir Weiss, Christian Terlizzi, Giuseppe Colucci, Luca Savelloni, Manuele Blasi, Gaston Brugman and Alessandro Crescenzi.
The winning strike came when Valiani received a high defense splitting ball out wide. After letting it bounce, the midfielder smashed it hard and low past a surprised Mattia Perin, beating the young shot stopper at his near post. It was the former Parma man's second goal of the season.
Pescara were gifted a chance to equalise when Matteo Contini tugged Ante Vukusic down in the box. The frontman dusted himself off and took the spot kick - Pescara's first of the season, only to see it saved by Gianluca Pegolo.
The fiery Cosmi was dismissed from the touchline after witnessing the penalty descision and seeing Emanuele Calaio spurn a chance to double the lead. The tactician kicked out at the advertising boards on his way to cool down.
Juan Fernando Quintero fashioned a couple of chances from set plays as the visitors tried and failed to find an equaliser. Their frustrations quickly boiled over, with two players dismissed in the dying minutes. First, Marco Capuano received a second yellow, then Damiano Zenon was given a straight red for throttling an opponent.
Reflecting on Stroppa's choice to leave, director of sport Daniele Delli Carri said:
"He no longer has the right spirit to continue and we accepted the resignation. Now we have to reflect on the situation. We didn’t expect this, despite the bad performance with responsibility shared out between players and Coach.
"Nobody thought about sacking him here. Today we did see the worst Pescara performance of the season.
"A resignation is unusual nowadays, but it seems there are still people out there willing to take responsibility for their mistakes."
Siena: Pegolo; Neto, Contini, Felipe; Angelo, Vergassola, Bolzoni, Rubin; Rosina (Sestu 66), Valiani (Del Grosso 87); Calaiò