Evergrande, who won the Asian title in 2013 and 2015, will play SIPG -- their closest rivals in the Chinese Super League -- over two legs in August and September.
Japan's Kawasaki Frontale also drew fellow J-League team Urawa Red Diamonds at an Asian Football Confederation (AFC) ceremony in Kuala Lumpur.
But in the West zone, Saudi sides Al Hilal and Al Ahli avoided each other as they were drawn with UAE's Al Ain and Persepolis of Iran respectively.
The Chinese clash, pitting Luiz Felipe Scolari's Evergrande against SIPG, who are coached by Andre Villas-Boas, will be closely watched.
Evergrande's chairman Liu Yongzhuo said: "The supporters would like to see two Chinese teams in the final. For the supporters (the draw) is a pity."
But he added: "We will be the champions again."
Evergrande, who have won the last six Chinese Super League titles, lead the domestic standings by just two points from SIPG.
The Shanghai side are spearheaded by their Brazilian attack of Hulk, Oscar and Elkeson -- who twice won the Asian trophy with Evergrande.
SIPG have been arguably the form team of the Champions League and they have already ousted Chinese opposition after beating Jiangsu Suning 5-3 on aggregate in the round of 16.
Last year's runners-up Al Ain, featuring Asian player of the year Omar "Almoory" Abdulrahman, will have home advantage in the first leg when they face Al Hilal.
Draw (played over two legs, home and away)
Quarter-final 1 (August 21-September 11): Al Ain (UAE) v Al Hilal (KSA)
Quarter-final 2 (August 22-September 12): Persepolis (IRI) v Al Ahli (KSA)
Quarter-final 3 (August 22-September 12): Shanghai SIPG (CHN) v Guangzhou Evergrande (CHN)
Quarter-final 3 (August 23-September 13): Kawasaki Frontale (JPN) v Urawa Red Diamonds (JPN)