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.
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.