The Russian fifth seed, bidding for a French Open-Wimbledon double after claiming the Roland Garros title this month, was forced to deuce in her opening service game but barely broke sweat after that in a one-sided contest lasting 58 minutes.
World number 247 Murray, no relation to the reigning men's singles champion, never looked capable of causing a shock as Sharapova dominated the rallies with her rasping groundstrokes.
Sharapova, who shot to stardom in 2004 when she beat Serena Williams to win the Wimbledon title, aged 17, said she was pleased to be off to a flying start after the quick turnaround from the claycourt season.
"It's such a quick turnaround," she told reporters. "You just want to be physically rested but also have enough preparation and practise going into Wimbledon, it's a thin line.
"But I've recovered mentally and physically."
Sharapova, trying to become the first woman to win both the French Open and Wimbledon in the same year since Serena Williams in 2002, will play Switzerland's Timea Bacsinsky next.
(Reporting by Michael Hann; editing by Martyn Herman)
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