Nadal, seeded second, lost 6-2, 7-5 to eighth-seeded Schwartzman, who will next play 12th seed Denis Shapovalov of Canada for a spot in the final.
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.
Hebei tied the game in the 98th minute when the referee awarded them a penalty after reviewing VAR. Marcao then converted it to complete a dramatic comeback. Enditem
Dominic Dale, the world number 70, also reached Stage Two after topping his group with two wins and one draw.
Alcantara will be only Liverpool's second signing of the summer after the arrival of left-back Kostas Tsimikas, who will provide backup to Andy Robertson, even though other sides, such as Liverpool's weekend rivals Chelsea, have been more active in the transfer market.
However, under the eccentric tutelage of coach Marcelo Bielsa, Leeds refused to lie down, and equalized in the 12th minute through Jack Harrison after a fine counter-attack.
The 35-year-old did not travel with his teammates to the Andean country on Monday after failing to recover from a shoulder injury, Flamengo said on Twitter.
"I always try to push him to do things he didn't know he can do. His potential is huge," the Pole said and spoke about sprint duels he has started in training in order to challenge the 25-year-old German international.
With just four minutes to go, Al-Ahli found a breakthrough as former Chelsea winger Marin drove into the heart of the Al-Shorta defense, and after a quick one-two with Abdulrahman Ghareeb, the German kept his composure to slot home from six yards.
Will Schalke 04 and Werder Bremen experience a change around after both fallen giants only narrowly survived a terrible last season?
Infantino also reiterated FIFA's prioritization of women's football through the recently-launched FIFA Women's Development Program and investment totaling one billion US dollars over the current four-year cycle.