After both exchanged serves in the following two games, a more experienced Zhang then delivered a dominant performance in the tie-break to seal the first set.
The 31-year-old, who is to face No. 7 seed Petra Kvitova in the next match, also became the first Chinese singles player since Li Na in 2012 to reach the fourth round at Roland-Garros.
He has also maintained Wolverhampton forward, Adama Traore in his squad, despite the striker, who was born close to Barcelona, also being called up by his parents' homeland, Mali.
"We did well on defense," said Inner Mongolia coach Zheng Wei, also assistant coach of China's national team, adding the team still needs to build its chemistry through more game time.
Also missing were injured Galatasaray goalkeeper Fernando Muslera and Atletico Madrid defender Jose Gimenez, who contracted the coronavirus.
As expected, head coach Gustavo Alfaro included Fenerbahce forward Enner Valencia and teenage Sporting Lisbon winger Gonzalo Plata in his 30-man squad.
Things got worse for Ole Gunnar Solskjaer's team as Anthony Martial was sent off for lashing out at Erik Lamela, and Harry Kane and Son made it 4-1 before halftime.
Leipzig remained offensively minded but for all that Julian Nagelsmann's men squandered a number of chances as neither Dani Olmo nor Nordi Mukiele was able to extend the lead.
Elsewhere, Eintracht Frankfurt came from behind to beat Hoffenheim 2-1. Borussia Monchengladbach wrapped its first victory of the campaign after easing 3-1 past rival Cologne. Wasteful Bayer Leverkusen shared the spoils with newly-promoted Stuttgart following a 1-1 draw and Leonardo Bittencourt's sole goal of the match helped Werder Bremen to edge newcomer Armenia Bielefeld. Enditem
The 51-year-old coach replaced interim coach Majid Namjoo Motlagh on the Tehran-based team.
The two-time Grand Slam winner committed just seven unforced errors throughout the one-sided encounter and broke her opponents six times.