After losing in the first round at Madrid last week, Sharapova needed 2 hours, 14 minutes Monday to claim her first victory on clay this season.
The former No. 1 player has been hampered by an injury to her right elbow this season. Against Kulikova, she converted only four of 22 break points.
Anastasia Rodionova of Australia also advanced with a 2-6, 6-3, 7-5 win over Avumi Morita of Japan.
Meanwhile, Gilles Simon of France has pulled out from the French Open because of his lack of fitness after returning from an injury.
Simon only started training last week after recovering from a knee injury.
The French tennis federation said Monday that Simon “feels inadequately prepared to play in an event as demanding as Roland Garros.” Simon will be replaced by Igor Kunitsyn of Russia in the main draw. The French Open starts Sunday.
Spaniard Rafael Nadal overtook Serb Novak Djokovic to move into second spot in the ATP world rankings released here on Monday.
The day after his 6-2, 7-6 (7/5) victory over Roger Federer in the Madrid Masters, Nadal moved into second spot behind the Swiss player.
American Venus Williams, beaten finalist in Madrid at the weekend, moved up one spot to second in the WTA rankings behind younger sister Serena on Monday.
Williams lost in straight sets to France's Aravane Rezai, who enters the Top 20 for the first time with a career high No. 16 ranking.
Russian Dinara Safina, beaten in the first round in Madrid, falls from fifth to ninth with compatriots Svetlana Kusnetzova and Elena Dementieva, Australian Samantha Stosur and Poland's Agnieszka Radwanska all moving up one spot.
