Brienza netted his second and Siena's third 20 minutes after his opener and then the game was all but secured four minutes into the second period when Luigi Giorgi made it 4-0.
It was at this point that the home fans protests got out of control as they threw flares onto the pitch and climbed atop barriers in the stadium.
Some sections of spectators left the ground but the game was temporarily suspended by the referee amid safety concerns of both fans and players.
When the game resumed almost an hour later, Genoa were able to pull one back through a Cristiano Del Grosso own goal but it was only to be a consolation goal on a dark day for the Serie A strugglers.
Lecce's 1-1 draw with Lazio means they are now just a point behind Genoa in the battle for survival.