Zhang, bidding to become just the second Chinese woman after Zheng Jie in 2008 to reach the last four, led 4-1 in the first set and held four break points for a 5-1 lead.
The 37-year-old Williams, who was also fined $17,00 for her remarks towards the umpire in last September's US Open final, is targeting a first Wimbledon title since 2016 and a record-equaling 24th grand slam victory.
Williams will next face Barbora Strýcová, 33, of the Czech Republic, The New York Times reports.
Ranked 50th in the world, Zheng had never previously won a match at Wimbledon, losing in the opening round five times.
As they've started to get a sense of what each other does and second guess each other's movements, the pairing are starting to look less like mixed doubles imposters and more like a force to be reckoned with.
Williams will take on unseeded Czech Barbora Strycova on Thursday afternoon for a place in her 11th Wimbledon final.
The tennis star was also not the only one fined during this year's Wimbledon tournament.
We are playing again on Wednesday and I'm looking forward to that.
Crucially, the American's trademark ability to raise her game to another level is back - and she has found her rhythm once more, the coach said.
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Tropical storms can form from old cool fronts that stall over the Deep South or along the Atlantic coast. It is forecasted to become a Tropical Storm by Thursday night, and a category one hurricane by Friday.
Serena Williams is coming off a three sets win over Alison Riske that took 29 games to decide. "I had to just button up and play hard".
Halep says she's not thinking about the past at Wimbledon this year; that's probably the right approach when it comes to her past against Svitolina. But in the second set, Riske broke for a 5-4 lead before holding serve to even the match.
Strycova's only other Grand Slam quarterfinal appearance came in 2014 at Wimbledon, where her serve-and-volley style of play is effective on the grass courts.
Trailing 4-1 she mixed up her game, serve and volleying on occasion, sneaking to the net when she could, slicing and dicing and generally making her opponent play the way she did not want to play.
Riske converted all five of her break points while Williams succeeded with just six of her 16 opportunities.
When she was knocked out at Roland Garros past year, Konta also took aim at the reporters.
Midway through the set, as the wind played havoc with her hair, Williams decided enough was enough, in more ways than one.
"I definitely have had loads of experiences, loads of people wanting me to die and things like that".
She was trying to process an agonizing quarterfinal defeat at Wimbledon, but British No.1 Johanna Konta labeled a reporter "patronizing" and "disrespectful" after he questioned her big-match mentality.