The German netted a perfect treble for the Bees in a resounding victory, which earned him a 9.5 Flashscore player rating.
Schade got things going with a clinical left-footed finish in the first half after initially showing a good bit of strength to hold off Bournemouth's Bafode Diakite.
He poked in his second into the roof of the net in the second half and completed his hat-trick with a well-taken header deep into stoppage time.
It is the second Premier League hat-trick of Schade's career, following his treble in a win over Leicester in November 2024.
Brentford are next in action on New Year's Day when they host Thomas Frank's Tottenham.