The second seed, who will next face fellow Russian Vitalia Diatchenko, was barely bothered by a cold in a late-afternoon canter on Court Philippe Chatrier.
"I'm getting over it, and hopefully it will pass by soon," Sharapova, who warmed up for Roland Garros by winning the Italian Open, told a news conference.
Sharapova, wearing a sailor shirt and a matching blue skirt, wasted chances to move 4-0 up as Kanepi broke back to trail 3-2, but normal service soon resumed.
The double Roland Garros champion won three games in a row to win the opening set having made only four unforced errors.
Kanepi buried a backhand into the net to hand Sharapova a break in the fourth game of the second set, but the Estonian broke back as the unforced errors started to pile up on the Russian's stats sheet.
Sharapova wasted one match point but a Kanepi double fault ensured a routine victory.
It was not too easy, however, on a windswept centre court.
"I had a tough opponent ahead of me. I knew that it was going to be tough and it wasn't going to depend on the tennis," she said.
"And the conditions were pretty difficult as well. So really, overall just happy I got through and have a day off tomorrow and I should be better by then."
Sharapova wasted no time in post-match interviews to the disappointment of the crowd who booed her out of the court.
"Of course I totally understand that, you know, everyone usually does post-interviews and answers a few questions to the crowd. It's absolutely normal," she said.
"I'm not making any excuses but I've got to do what I have to do."
(Reporting by Julien Pretot; Editing by Martyn Herman and Justin Palmer)
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