The Russian second seed, playing for the third day in succession after needing two days to complete her second round because of rain, was forced into a scrap after initially looking a class above her 43rd-ranked opponent.
Sharapova trailed 4-1 in the second set, clawed back to 4-4, then fell 5-4 behind with Zheng serving to level the match but turned up the volume of her grunting and her play to avoid being extended further.
The 26-year-old wrapped up victory when Zheng netted a forehand service return, moving through to a last-16 clash against American Sloane Stephens, who beat Marina Erakovic 6-4 6-7(5) 6-3.
Third seed Victoria Azarenka stuttered into the last 16 of the French Open but her title credentials were given a rigorous examination in a 4-6 6-3 6-1 win over a spirited Alize Cornet.
For large periods of the encounter, France's Cornet out-fought the double Australian Open champion and looked much sharper around the court.
Cornet, seeded 31, took the first set and both players struggled to find consistency on their serve, frequently exchanging breaks, as the sun made a rare appearance at Roland Garros.
The pair then went toe-to-toe before the Belarussian found her rhythm and broke Cornet's resolve, taking the second set and running away with the third.
"I'm not surprised by how she played, she showed what a terrific player she can be," Azarenka said in a courtside interview. "That's the best tennis she has played against me."
Azarenka's consistency and greater firepower, however, ultimately wore down Cornet.
"She's a machine, a juggernaut," Cornet said. "She plays the same from the first to the last point.
"It's my feeling that I was knocked around everywhere by her topspin.
"What's frightening is I dropped one or two games but that's enough for your head to go under the water."
Azarenka will now face former champion Francesca Schiavone, who put in an eye-catching performance to beat France's Marion Bartoli 6-2 6-1.
With all eyes on defending champion Maria Sharapova and world number one Serena Williams, Italian Schiavone, the 2010 Roland Garros winner, had gone unnoticed until she ended Bartoli's run in ruthless fashion on Court Suzanne Lenglen.
Bartoli fought until the end but there was little she could do against Schiavone's repertoire of sliced backhands, spinning forehands and cunning lobs that got the better of the Frenchwoman after 78 minutes.
2-Maria Sharapova (Russia) beat Zheng Jie (China) 6-1 7-5
3-Victoria Azarenka (Belarus) beat 31-Alize Cornet (France) 4-6 6-3 6-1
Jamie Hampton (U.S.) beat 7-Petra Kvitova (Czech Republic) 6-1 7-6(7)
18-Jelena Jankovic (Serbia) beat 9-Samantha Stosur (Australia) 3-6 6-3 6-4
12-Maria Kirilenko (Russia) beat Stefanie Voegele (Switzerland) 7-6(3) 7-5
Francesca Schiavone (Italy) beat 13-Marion Bartoli (France) 6-2 6-1
17-Sloane Stephens (U.S.) beat Marina Erakovic (New Zealand) 6-4 6-7(5) 6-3
Bethanie Mattek-Sands (U.S.) beat Paula Ormaechea (Argentina) 4-6 6-1 6-3