Two minutes into the second half, Matheus Pereira curled home an excellent free-kick to level the scores, but Everton were soon back in front when Michael Keane prodded home from close range, and the home side then ran riot, with Calvert-Lewin netting twice more to complete his first hat-trick for the club.
The question of how to stop the 2013 and 2020 treble winning Bavarians remains unanswered. Most competitors expect the coach Hansi Flick's team to repeat.
18-year-old Lorenzo Musetti of Italy, who had upset three-time Grand Slam winner Stanislas Wawrinka of Switzerland and Japan's top player Kei Nishikori in the tournament's opening two rounds, lost to Dominik Koepfer of Germany 6-4, 6-0.
Flamengo had never before lost a Copa Libertadores match by a five-goal margin. Previously, their worst showing in South America's premier club competition was a 5-1 capitulation to Gremio in 1984. Thursday's result was also the heaviest defeat by defending Copa Libertadores champions.
Dortmund gained momentum and pinned Duisburg in their territory before Thorgan Hazard's back-heel pass found youngster Jude Bellingham, who made no mistake to make it 2-0 from inside the box in the 30th minute.
Stoppila Sunzu (R) of Shijiazhuang Ever Bright competes during the 11th round match between Tianjin Teda and Shijiazhuang Ever Bright at the postponed 2020 season Chinese Football Association Super League (CSL) Suzhou Division in Suzhou, east China's Jiangsu Province, Sept. 16, 2020. (Xinhua/Li Bo)
Arsenal continued their winning start to the season against West Ham with goals from Alexandre Lacazette and young striker Eddie Nketiah, who scored the winner five minutes from time after Michail Antonio had equalized just before the break. Enditem
Top seeds Novak Djokovic and defending champion Rafael Nadal, who have first round byes, will begin their campaigns on Wednesday.
"Unfortunately, I won't be able to play the French Open this year. My hamstring is still sore, so I won't have enough time to prepare for the clay," Osaka said on Twitter and Instagram.
Elsewhere, Russia's Andrey Rublev beat Argentinian qualifier Facundo Bagnis 6-4, 6-4 and will meet Poland's Hubert Hurkacz in the next round.
Flamengo remain second in the group with six points from three matches but with a negative goal difference.