Sharapova, who impressed on the clay in Stuttgart recently, defeated American Christina McHale in a hard-fought match.
The Russian booked her place in the third round with a 7-5 7-5 victory.
Fourth seed Petra Kvitova also won her second-round match but again was made to fight.
The Wimbledon champion eventually saw off Anastasia Pavlyuchenkova 7-5 6-4.
Fifteenth seed Sorana Cirstea also made tough work of her opening tie, finally beating former world number one Jelena Jankovic 6-3 4-6 7-6 (7/4).
However, Dominika Cibulkova brushed aside Mirjana Lucic 6-1 6-2 and Italy's Flavia Pennetta defeated Maria Kirilenko 6-1 7-6 (7/2) to move into the second round.
Elsewhere, Spain's Silvia Soler-Espinosa beat Italy's Alberta Brianti while American Sloane Stephens defeated Anna Chakvetadze.