Safarova – who won the 2005 title in three sets against China's Li Na – produced an outstanding comeback to beat Slovakian Magdalena Rybarikova 4-6 6-0 6-0.
Both players struggled for rhythm in a first set riddled with breaks, but it was the sixth seed trailing after the opener at the WTA International event.
The world number 26 drastically improved in all areas after her early setback, though, as she incredibly reeled off the next 12 games.
Safarova continued to punish Rybarikova's sloppy serving, with her three breaks in the second setting up a deciding set.
Any hope of a tight finish was blown away by Rybarikova, who won just five of 18 points on serve in both the second and third set.
Wickmayer won slightly easier and also finished with a flourish in a 6-4 7-5 triumph over Poland's Urszula Radwanska.
The Belgian claimed the 2009 title against Russian Ekaterina Makarova and moved into the second round, despite serving 10 double faults on the clay.
Radwanska, who has battled a shoulder injury recently, has now been knocked out of the first round in her last six tournaments.
After taking the first set thanks to three breaks, Wickmayer trailed 3-5 in the second set, only to win the last four games to claim victory.
Other first-round results saw Kazakh Yaroslava Shvedova beat Italy's Karin Knapp 6-2 6-4, while Tunisian wildcard Ons Jabeur cruised to a 6-3 6-1 win against Portugal's Maria Joao Koehler.
And Serbia's Bojana Jovanovski proved too good for Puerto Rico's Monica Puig, winning a tight tussle 6-4 4-6 6-4 in two hours and 18 minutes.