Williams, who beat Anna Schmiedlova in the previous round, was broken in the first game of the first set, but battled back to secure three breaks of her own to lead 5-1.
Dellacqua then got the better of her opponent again, breaking twice to close the gap. However, Williams was able to find a way through the Dellacqua serve to take the first set.
The American was broken three times in the second as Dellacqua managed to level the match.
The third set went with serve in the first five games, but Williams broke, before suffering the same fate to leave it at 4-4.
After holding serve, Williams secured the win with yet another break.