Hingis, competing in her second tournament after undergoing surgery to repair torn and damaged ligaments in her left ankle, is seeded fifth. After taking the first set from Smashnova, she raced to a 5-0 lead in the second before holding on.
Hingis' second-round opponent will be unseeded American Alexandra Stevenson, who ousted Croatia's Jelena Kostanic, 6-3, 7-5.
The 21-year-old from Switzerland had not played since early May in Hamburg, where she reached the semifinals and won the doubles title with Barbara Schett.
In her first event back, Hingis advanced to the quarterfinals last week in Montreal before falling to Dokic.
In early action Monday, German qualifier Angelika Roesch surprised eighth seed Elena Dementieva of Russia, 6-3, 1-6, 6-3. The struggling Dementieva is heading to the U.S. Open having lost four of her last five matches.
Stevenson was one of three Americans in action Monday. Qualifier Laura Granville rallied past Daja Bedanova of the Czech Republic, 3-6, 6-4, 6-1, but Lisa Raymond was ousted by Russia's Elena Bovina, 4-6, 6-1, 6-2.
Williams is trying to capture her fourth straight title here. A year ago, she defeated Davenport in the final to make it three in a row and maintain her perfect record at the Connecticut Tennis Center at Yale.
The 22-year-old Williams had her 20-match Wimbledon winning streak snapped in July when younger sister Serena dethroned her in the final at the All-England Club and overtook her atop the world rankings.
Later that month, however, Venus Williams captured her first singles title in three months at Stanford, then made it two in a row at San Diego.
The runner-up here twice in the last three years, Davenport will try to win this event for the second time. Her lone success came in 1997, the only year the tournament was held in Atlanta and the last time it took place outside New Haven.
Davenport returned to the WTA Tour at Stanford after being sidelined for nearly nine months as she recovered from knee surgery.
The former world No. 1 is 11-3 since her return, reaching the semifinals at Stanford and San Diego before advancing to the final at Los Angeles.
Dokic is seeking her third title of the year, having won the Sarasota claycourt event and the Birmingham grasscourt tournament.
After winning three WTA titles in 2001, Henin's lone success this year came in May at the German Open claycourt event. She also lost to Venus Williams in the Wimbledon semifinals in a rematch of the 2001 final at the All-England Club.
Celebrity Families of 2014 [PHOTOS]