The second-seeded Russian, who is seeking to become the second woman to win consecutive titles in the past decade, cruised through her opening match and will be a huge favourite against Dellacqua, the world number 90.
"It's kind of weird playing opponents you haven't played against," Sharapova said.
"I know she is a lefty and I've seen her play a little bit on some of the matches on TV. I haven't seen too much to know really what she does well and not. So I think it's just going to be up to me to figure it out as soon as I can."
In the men's event, Americans Andy Roddick and James Blake are both in second-round action.
Fifth seed Roddick, the champion in 2003, takes on Argentine Jose Acasuso, while sixth seed Blake, a quarter-finalist in each of the past two years, plays Frenchman Fabrice Santoro after Sharapova's match in the night session.
Former champions Svetlana Kuznetosva, the fourth seed, and Martina Hingis, seeded 16, play second-round matches, while men's fourth seed Nikolay Davydenko faces a tough test against German Nicolas Kiefer.