Belgium's Flipkens, who defeated Czech Lucie Hradecka in last year's Quebec finals, fell by the wayside at the hands of Slovenian Polona Hercog 6-3, 6-1 at Quebec's Laval University.
Safarova, meanwhile, moved on as expected against Georgian Anna Tatishvili in 6-3, 6-2 fashion, while Czech Barbora Zahlavova Strycova -- who won the 2011 tourney -- dispatched Greek Eleni Daniilidou 6-3, 7-5.
Elsewhere on Day 2, Kazakhstan's Sesil Karatantcheva bested Swiss fellow qualifier Amra Sadikovic 6-3, 6-4 and French qualifier Julie Coin got past Portugal's Michelle Larcher de Brito 7-6 (7-5), 7-5.
Also Tuesday, Croatia's Mirjana Lucic-Baroni whipped Canada's Sharon Fichman 6-4, 6-0.
Megyn Kelly: Santa Claus and Jesus are both white men
Video of Victoria’s Secret models trying to 'twerk' hits Instagram