One of 32 players to receive a first-round bye, Williams improved to 42-5 all-time here, including a win over world No. 1 Justine Henin in last year’s championship match. The 26-year-old also claimed three consecutive titles here from 2002-04 and was a runner-up to older sister Venus Williams in 1999.
The former world No. 1 and eight-time Grand Slam champion never faced a break against Gallovits and won 23-of-25 (92 percent) first-serve points. Her third-round foe will be No. 27 Flavia Pennetta, a 6-4, 6-2 winner against Anastasia Rodionova.