The Russian world number five, defending champion on the clay in the Spanish capital, was the latest big name to fall after Grand Slam winners Justine Henin, Maria Sharapova and Svetlana Kuznetsova lost their first-round matches.
In a topsy-turvy encounter, Safina and Zakopalova, the world number 88, each claimed seven breaks of serve but the 28-year-old from Prague dominated the tie-breaks, winning the first 7-1 and the second 7-3.
Safina, who slipped from three to five in the updated rankings on Monday, has lost in the Roland Garros final the past two years and has yet to claim a Grand Slam title despite rising to the top of the rankings last year.
Venus Williams, the fourth seed, had a much easier passage into the last 16 when she beat Russian Vera Zvonareva 7-5, 6-3.
World number two Caroline Wozniacki, who lost to Safina in last year's final, looked to have recovered from a recent ankle injury and brushed aside Czech qualifier Petra Kvitova 6-4, 6-2 quickly.
