They took to the court at the Mouratoglou Tennis Academy in the south of France with black t-shirts emblazoned with the movement's message.
The Italian beat Brown 3-1, while Alexei Popyrin beat Elliot Benchetrit by the same score.
Feliciano Lopez beat Lucas Pouille in sudden death with the score tied at 2-2.
Lucas Pouille and David Goffin are among the other players taking part in the event, which has its matches split into quarters with a timer ticking down to zero, encouraging swift play.
Brown and Berrettini wear Black Lives Matter shirts at Ultimate Tennis Showdown