The American took advantage of early breaks in each set to overcome an inexperienced but plucky opponent who rallied well and struck some fine volleys.
Davenport broke to lead 2-0 in the first set, but then had to fight off three break points at 3-1 and then another as she served for the set.
Davenport then broke for 1-0 in the second set and comfortably maintained her lead.
"I'm never one that necessarily plays their best right off the bat," said Davenport. "It took a little while to settle into the conditions and how Rika plays, but I do feel I started to improve some things in the second set."
Davenport is hoping to quickly put her disappointing quarter-final defeat at the U.S. Open behind her.
"Any time that a Grand Slam is over and you feel like you have a chance to win, there's obviously a let-down when it doesn't happen that way," she said.
"But coming here, it's been a really great opportunity to relax and get back out on the court right away."
Fourth seed Francesca Schiavone overcame Spain's Laura Pous Tio 6-3, 6-4, the feisty Italian untroubled by her hard-hitting but erratic opponent.
