Four-time champion Serena narrowly avoided an embarrassing third round exit on Saturday, the second week of Wimbledon, as she fought back from a set down to grind out a gritty 6-7 (5/7), 6-2, 9-7 victory over the tenacious Zheng.
While the sixth-seeded American would have preferred a routine straight sets win, she is convinced the experience of coming back from the brink will make her even more battle-hardened in the remaining four matches that stand between her and a fifth Wimbledon title.
"It definitely helps me to realise that's it's not going to be easy going forward. I just have to stay focused," former world number one Serena said.
"Everyone's trying to win, but I can win matches like this. Not that I've ever doubted that, but it's always good to have that reconfirmation."
Surviving a tough examination against Zheng was also important for Serena's morale as she tries to erase the memories of a confidence-denting shock three-set defeat against France's Virginie Razzano in the French Open first round last month.
"I was definitely way more calm than I was when I lost in my last long match," Serena said.
"With any loss, you have to really get that feeling of confidence back. You know, it's not easy, especially when you're doing so well, to lose and then to try to come back.
"It's all mental. I'm just trying to do the best that I can do.
"I thought, 'Serena, just relax and be calm'. I felt good. I never felt like I was going to lose this match."
Williams may need to be at her very best to progress beyond the last 16 because she faces in-form Kazakh wild card Yaroslava Shvedova on Monday.
Shvedova completed the first Golden Set in Grand Slam history by winning all 24 points in a 6-0 first set whitewash against Sara Errani in the third round.
Shvedova, the world number 65, hit 14 winners and took just 15 minutes to demolish Italian 10th seed Errani, the French Open runner-up, in an incredible first set on Court Three.
The 24-year-old, the Wimbledon doubles champion in 2010 and twice a French Open quarter-finalist, closed out the win in the second set and Williams was stunned when she learned exactly what her next opponent had accomplished.
"I never knew that existed. I was like, 'What does that mean?' I immediately thought, She won all four in a row and the Olympics? I thought that wasn't possible. That's the only golden thing I know of," she said.
Endinf a drought
"Hopefully I'll be able to win a point in the set. That will be my first goal, and then I'll go from there."
After winning 13 Grand Slams in her illustrious career, Serena has gone without a major title since landing her last Wimbledon crown in 2010.
But the 30-year-old looks in the mood to end that drought.
Serena, who will spend her Sunday off by tuning into the Euro 2012 final between Spain and Italy, served a Wimbledon record 23 aces against Zheng and doesn't seem especially worried about facing Shvedova.
"The serve definitely helped me out because I wasn't doing my best on my return. So it's good to know that I can rely on the serve," she added. Sapa-AFP