The Chinese 12th seed, who reached the US Open last eight in September and ended the year as the WTA Tour's most improved player, barely put a foot wrong in the 59-minute masterclass on Rod Laver Arena and will meet Russian Anna Kalinskaya (25) next.
"Second time in a quarter-final, I have more experience but I want to focus on the moment," said Zheng, who can emulate her idol Li Na by winning the tournament and has received plenty of tips from her compatriot who is at Melbourne Park.
"That's what she told me to do... She's a really classic, powerful woman. She looks much more beautiful than when I saw her on TV when I was young."
Both players revved up their backhands early in the opening set but it was Zheng who drew first blood with a stunning winner down the line and she saved a break point to power ahead 3-0, tightening her grip on the contest from there.
Zheng then reeled off the points to blank her opponent and started the second set in a menacing mood but Dodin opened her account with a hold.
The unseeded Frenchwoman raised her arms and smiled as fans cheered but Zheng regained focus after the duo swapped breaks to rack up a 4-2 advantage to run away with the match, which she wrapped up when Dodin crashed a return into the net.
