Di Maria turned provider in the second half as his free-kick set up for Marquinhos's header to seal the game 3-0.
Dortmund broke the deadlock courtesy of two 17-year-old youngsters, as new arrival Jude Bellingham passed into the path of Giovanni Reyna, who drilled the ball right-footed into the far corner in the 35th minute.
Zinedine Zidane's side didn't play in the first round of matches one week ago, after their game at home to Getafe was postponed in order to allow them more time to recover after their participation in last season's Champions League in August.
"The design of Beijing Workers Stadium considers not only the Asian Cup, but also other important events and the daily operation of the club. Some of the designs even go beyond the AFC standard," said Zhu Xiaodi, chief architect of Beijing Institute of Architecture Design.
Mo Youxue of Guangdong competes during the men's 4X100m relay final on Day 2 of the 2020 Chinese National Athletics Championships in Shaoxing, east China's Zhejiang Province, Sept. 16, 2020. (Xinhua/Jia Yuchen)
But just when it appeared as if Leeds would take a well-deserved point back to West Yorkshire, a loose challenge from record signing Rodrigo resulted in another penalty which Salah tucked away with unerring accuracy.
The following games conclude the first round on Sunday: RB Leipzig face Mainz, while Wolfsburg host Bayer Leverkusen. Enditem
The Foals responded but neither Stefan Lainer nor Lars Stindl was able to overcome Burki before the half-time whistle.
Stage One will be played across two blocks of eight days: September 13-20 and September 28-October 5.
"The finish was impressive, playing with nine against 11. We showed an incredible mentality. It was a deserved victory after a crazy match. I am very proud," the German coach said.
Julian Nagelsmann's men gained momentum and doubled their advantage only four minutes later when Dani Olmo had sufficient space at the edge of the box and chipped the ball into the path of Poulsen, who headed the ball over Zentner.