The 17-year-old Russian, seeded fourth, crunched 15 winners on her way to victory in exactly an hour.
But though she looked every inch a potential champion, Sharapova said she had plenty of room for improvement.
"Like I've said before many times, I cannot win everything," she said.
"You never know what can happen, and I'm still developing my game. It's not that (because) I won a Grand Slam, all of a sudden I'm going to win everything. I understand that. And that's why my game is still a work in progress."
Karatantcheva, the world number 110, showed few signs of nerves in just her second Grand Slam event as she matched Sharapova in the early stages.
The Russian sprayed 26 unforced errors around the court, but once she'd taken the first set, the result was never in doubt and a forehand over the baseline from the Bulgarian sealed Sharapova's victory.
"She's a very aggressive player, attacked her serve. I just played a good, solid first round match," Sharapova said.
The Russian will meet either American Lindsay Lee-Waters or Hungarian qualifier Zsofia Gubasci for a place in the third round.
