Ukraine-born Lepchenko, now a naturalized U.S. citizen and a member of the U.S. Olympic team, never faced a break point and won despite making only 55 percent of her first serves.
“It was pretty difficult out there and I'm still trying to get used to the conditions and still trying to find my game,” Lepchenko said. “I'm happy the way it ended up.”
Scheepers provided an opening in the second set when she double-faulted in the third game to give Lepchenko a 2-1 lead.
No. 1 seed Marion Bartoli of France will see play her first match when she faces American Vania King in a second-round night match.
Lepchenko will next face No. 4 seed Nadia Petrova of Russia, a 6-4, 6-3 winner over American qualifier Alexa Glatch.
Qualifier Chan Yung-jan of Taiwan moved into the quarterfinals with a 6-3, 7-6 (2) win over Britain's Heather Watson.