Scheepers needed just more than an hour to eliminate Cirstea 6-3, 6-1, piling up three breaks in each set.
Cirstea was good on just 52 percent of her first serves and had 10 double faults, a problem serving that Scheepers took advantage of. She won 60 percent of the points when Cirstea served. Scheepers allowed Cirstea to win just four points on serve in the second set.
Monday's other main-draw match was even more lopsided as Maria-Teresa Torro-Flor dispatched Arantxa Rus 6-1, 6-1. Torro-Flor took 70 percent of the points on serve and didn't face a break point. She finished five of her 12 break chances on the match.
Scheepers and Torro-Flor will play each other in the second round.
The tournament, officially called the Grand Prix sar la Princesse Lalla Maryem, also lost its top seed Monday.
No. 1-seded Dominika Cibulkova withdrew and Tsvetana Pironkova was given a No. 9-seed and inserted in Cibulkova place in the draw. Cibulkova played two matches last weekend in Moscow for the Slovak Republic against Russia in the Fed Cup semifinal.
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