The three-time French Open champion and 23-time Grand Slam victor will next take on Australia's Ash Barty in the second round.
Williams will face Germany's Julia Goerges for a place in the last 16 on Saturday.
Czech Pliskova made the semi-finals here a year ago, and may fancy her chances against Sharapova, who had to fight hard to get past Richel Hogenkamp and Vekic in her first two matches.
"It's just incredible", she said.
"I'm very happy. She played really well, she made a lot of aces".
'I think any time you play against Serena you know what you're up against, ' the 28th seed said.
While trying to surpass Margaret Court's record of 24 Grand Slam titles might be one of the reasons she pushed herself to get back on court despite all her complications in childbirth, she also wants to see if she recover her pre-pregnancy form.
Federal Bureau of Investigation wants you to reboot your router to defeat Russian malware infection
They say VPNFilter is able to make the routers inoperable and can also potentially collect information from the router. Stage 1 is installed first and allows the malware to stay persistent even when the router is rebooted.
Lionel Messi says Argentina are not favourites to win in Russian Federation
Argentina , meanwhile, are in Group D with Iceland, Croatia and Nigeria. "In a World Cup , logic is nearly never given". After that, I have always said that I want to play football in Argentina but I don't know if it will happen.
White House Imposes Tariffs on US Allies EU, Canada And Mexico
Europe, Canada, and Mexico are not China, and you don't treat allies the same way you treat opponents", said Sen. The tariffs will also cause major economic disruptions in the US, Canada, Mexico, and the EU .
As she served for the match, she slipped into the net, righting herself sporting an embarrassed smile.
Williams hit just three winners while 22-year-old Barty could afford to bide her time, just two winners and four unforced errors coming from her side. The same continued into the first game of the second set, and Serena was quickly broke. One break was enough for the Australian to take it 6-3.
"Supermama is back. Second time is better still".
Halep leads their head-to-head 6-1, including a clash in the semi-finals in Paris in 2015.
Spaniard Rafael Nadal, got the better of Guido Pella of Argentina, 6-2, 6-1, 6-1 to progress to the third round, thereby dominating on his favourite clay court surface.
As fans may already know, the sisters played against Shuko Aoyama and Miyu Kato at the French Open today, and they managed to come out victorious.
"I´ve been asked to put a skirt on over leggings many times".