Sharapova underlined her pulling power with organisers confirming they had sold out all of the day sessions for the entire tournament just minutes before she stepped on court for her first round match.
A limited number of tickets for the three night sessions were left available, though all of Sharapova's matches will be played during the day and organisers said it was the first time the tournament, with a total prize pool of just $220,000, had been effectively sold out by the first day.
Sharapova received an enormous cheer from the 3,200 fans packed around the revamped centre court.
The 23-year-old Russian's original first round opponent Carla Suarez Navarro was changed after fifth-seeded Latvian Anastasija Sevastova withdrew with illness, making the Spaniard the eighth seed.
Italy's Brianti, who had earlier lost to Britain's Heather Watson 6-2 6-2 in qualifying, was then promoted to the main draw.
Katie O'Brien was beaten 6-0 6-3 by Thailand's Noppawan Lertcheewakarn in qualifying but fellow Brit Anne Keothavong came back from a set down to defeat Romania's Edina Gallovits 6-7 6-4 6-0 to reach the last 16.
The 25-year-old Russian, who had what she described as a year to forget in 2010 and finished outside the top-20 for the first time since 2004, initially had difficulties with her young New Zealand opponent as Jones lifted her game in response to the raucous crowd.
Kuznetsova, however, took stock, adjusted her tactics and patiently wore down Jones in the second set.
"The circumstances were very hard for me, I hadn't played a match for three months then I met a player who was motivated and had nothing to lose," Kuznetsova said after the 86-minute match. "She had the home crowd, I had never played her before and had no idea what to expect.
"For almost the (whole) first set I had to watch and adjust to how she was playing. She was playing good and aggressive, and had nothing to lose... but (in the second set) I was able to put more pressure on her."