It was a bizarre way for the Frenchman to lose the jersey which he had kept for three days after winning the stage two.
Flamengo netted twice in quick succession after the restart: first with a stunning first-time effort from playmaker Everton Ribeiro and then with a cool Arrascaeta finish after a counterattack.
The match ended in a goalless draw, despite Botafogo's 17 shots on goal to Coritiba's seven.
Valter, 22, broke free during the final few kilometers and the peloton was unable to catch him.
Nationwide demonstrations against what activists have described as police brutality and systemic racial inequality have broken out over the past few months, particularly after police killed George Floyd and shot Jacob Blake. Enditem
"These are needless deaths. Needless. We should be similar to most countries on the planet, and yet, we are an embarrassment, and a tragic embarrassment," Lurie added.
Lurie took charge of the Eagles in 1994, and led the team to its first Super Bowl title in 2017.
The Tour, which was moved from its original date in July due to the COVID-19 pandemic, ends in Paris on September 20. The next stage is a 191km ride from Le Teil to Mont Aigoual. Enditem
"So you have to make her in trouble. That's what I like and it was a great challenge for me today. I did well in this challenge and I can take the happiness for it, and now I'm after another one."
Garcia looked untouchable in the first set and for much of the second, blasting 30 winners and breaking Pliskova's serve three times en route to a 6-1, 7-6 (2) victory.
The hosts added their third goal when Daniel Sampaio latched onto Marco Antonio's pass to slot home in stoppage time.