Schalke's U.S. midfielder Weston McKennie wore an armband in Saturday's defeat to Werder Bremen bearing the words "Justice for George".
Mr Floyd was an unarmed black man who died after a Minneapolis police officer kneeled on his neck for greater than eight minutes as he advised them "I can't breathe".
Thuram's move was quickly backed by his manager Marco Rose.
Alassane Plea, who assisted Thuram's second goal, then scored the fourth on the 81st minute to wrap up a flawless win.More news: Locust attacks: Delhi issues advisory with list of preventive measures
England global Sancho, who went on to complete a hat-trick as Dortmund dished out a 6-1 thrashing, was booked for removing his playing jersey.
Schmelzer then scored their fifth when he converted a low Axel Witsel cross on 89 minutes.
An England worldwide winger who continues to catch the eye in Germany - with a first senior hat-trick recorded on his most recent outing - has seen speculation build when it comes to a possible return to his homeland being made.
The 22-year-old Thuram headed in at the far post from fellow Frenchman Plea's cross in the 41st minute after Florian Neuhaus had put the hosts ahead in the 17th with a solo run.
Union's Swedish striker Sebastian Andersson pulled one back early in the second-half after being left unmarked.More news: WeTransfer file sharing website banned in India on grounds of ‘national security’
After the final whistle, the Gladbach squad celebrated in front of stands filled with cardboard figures of fans.
After a 3-1 defeat to Leverkusen last weekend and a goalless draw with relegation-threatened Werder Bremen on Tuesday, this was an important win for Gladbach.
It lifted them to third in the table, but RB Leipzig can take their place if they win at Cologne on Monday.
Now you can read the Jamaica Observer ePaper anytime, anywhere.More news: Sunak throws lifeline to self-employed by extending support scheme