"Wimbledon may be my last tournament before the Olympics because I will go back to China instead of the playing the hard-court season."
It was a good day for China as Zheng's compatriot Li Na also won, seeing off Anastasia Rodionova 3-6, 6-0, 6-1.
Li proved she is fully recovered from her injury woes as she came from a set down to defeat Rodionova.
The 27-year-old was the first Chinese player to reach the quarter-finals of a Grand Slam singles when she made the last eight at Wimbledon in 2006.
But she missed the second half of 2007 with a rib injury and was sidelined again for four months with a knee problem.
This was only her second tournament since February but she swiftly shook off the rust to set up a second- round clash against Russia's Anatasia Pavlyuchenkova who, at 16, is the youngest player to have come through qualifying.
Li lost the first set as she eased her way back into Grand Slam action but took control in the second set and won it without losing a game.
It was an impressive display of power hitting and Li kept her foot on the gas, breaking in the first game of the decider and again in the third.
Rodionova, a Russian now seeking Australian citizenship, had no answer to Li's relentless ground game and was blown away in the final set.
Yuan Meng couldn't follow Li and Zheng's example as she lost to France's Nathalie Dechy 7-6 (7), 3-6, 0-6.
Yuan, 23, went out in the first round on her only previous visit to Wimbledon in 2006 and didn't fare any better this time.
She had the chance to take control of the match after winning the first set on a tiebreak.
But Dechy is a former Australian Open semifinalist and her class told as she quickly took the second set.
The final set followed a similiar pattern as Dechy broke earlier and raced through to a second-round match against top seed Ana Ivanovic.
(Agencies via China Daily June 24, 2008)