Azarenka dispatched Andrea Hlavackova 6-3 7-6, Sharapova saw off Klara Zakopalova 6-4 6-3 and Williams , seeded nine and making her first European appearance of the season, thumped unseeded Russian Anastasia Pavlyuchenkova 6-2 6-1.
Serena eased through a day after her sister Venus was knocked out by Germany's Angelique Kerber.
Sharapova, who beat world number one Azarenka in the Stuttgart final last month, was first up on the unfamiliar blue clay of the Manolo Santana show court.
The colour is a controversial innovation at this year's edition of the event and has prompted complaints from Novak Djokovic, Rafa Nadal and others.
With the sliding roof closed to keep off the morning drizzle, second-seeded Russian Sharapova found her range and broke Zakopalova's serve in the opening game.
The three-times Grand Slam singles champion wobbled when serving for the match at 5-2 in the second set but broke again in the next game for a comfortable win.
Sharapova next meets another Czech, unseeded Lucie Safarova , who beat Spanish wild card Carla Suarez Navarro 6-3 6-4.
Sharapova said the blue clay was a little more slippery than its red counterpart but added that she generally approved of the decision to switch colours, which organisers argue makes it easier to follow the yellow balls on television.
"I did feel a bit of a difference with the amount of clay that is on the court and the bounces were a bit off, especially the first couple of days of practice, but I feel like it's got better and settled in a little bit," she said.
"You just have to work on your balance a bit more," added the 25-year-old world number two, who will be chasing the only Grand Slam that has eluded her at the French Open starting later this month.
Belarusian Azarenka had newly-appointed adviser Amelie Mauresmo watching from her box alongside coach Sam Sumyk and made short work of Hlavackova, who needed treatment on her left thigh midway through the second set.
Like Sharapova, top seed Azarenka missed a chance to serve out the match in the second set but went on to take the tiebreak 7-2 and will next play Ana Ivanovic of Serbia, a former world number one, who is seeded 13 and beat Russia's Nadia Petrova 7-5 6-1.
"It is a little bit slippery but it's the same for everybody," Azarenka, who lost to Petra Kvitova in last year's final, said when asked about the blue court.
"I don't like to complain about the surface, it is what it is," the Australian Open champion added.
"You have to deal with it and nobody's going to change it now so everybody is playing in the same conditions."
Kvitova plays her second-round match against Czech qualifier Lucie Hradecka on Wednesday.
In other second-round matches, American Varvara Lepchenko beat Israeli Shahar Peer 7-6(2) 6-4, to set up a third-round clash with Spain's Anabel Medina Garrigues after she beat Sorana Cirstea of Romania 6-1 3-6 7-5.