Jankovic, the 2007 champion here and former world No. 1, needed a little over two hours to finally put away Gallovits at the $700,000 event.
The second seed, who won her 12th career title last month in Indian Wells and had a first-round bye here, had her serve broken four times by Gallovits on the green clay of the stadium court.
Russian seventh seed Vera Zvonareva booked her spot in the third round with a 6-2, 6-0 rout over Paraguay’s Rossana de los Rios, while Canada’s Aleksandra Wozniak outlasted Catalina Castano of Columbia 6-2, 4-6, 6-4.
In first-round matches, Russians Elena Vesnina and Vera Dushevina and Patty Schnyder of Switzerland won.
Following the withdrawal of world No. 1 Serena Williams, second ranked Caroline Wozniacki of Denmark heads the Charleston field.
