The three gold medal contenders were among just a handful of winners after downpours washed out much of the day's play at Wimbledon and closed the Centre Court roof.
Olympic tennis had not been played indoors since Stockholm 1912, but Murray and Sharapova shrugged off the chaos as both enjoyed the first Olympic wins of their careers.
Britain's Murray beat Switzerland's Stanislas Wawrinka 6-3, 6-3 and French Open champion Sharapova thrashed Israel's Shahar Peer 6-2, 6-0. Serbia's Djokovic, the second seed, beat of Italy 6-7 (7/9), 6-2, 6-2.
It was a cathartic victory for Murray, who was back on Centre Court for the first time since crying tears of frustration after his Wimbledon defeat against Roger Federer exactly three weeks ago.
The 25-year-old, who had hoped to become the first British man to win Wimbledon sincein 1936, brushed aside Federer's compatriot to set up a last-32 clash with Finland's or India's Somdev Devvarman.
Murray admitted he had been keen not to repeat his first round exit in Beijing at the hands of Taiwan's Lu Yen-Hsun.
"I was disappointed with the way I played in Beijing. I didn't understand what the Olympics meant to me," he said.
"I know how much that loss hurt me and I wanted to come here as well prepared as I could be. Today was a good start."
For Sharapova, beating Peer meant more than just a place in the last 32 as the Russian finally got to savour a taste of the Olympic experience -- as she chases a career "Golden Slam" of all four grand slam titles and Games gold.
Sharapova missed Beijing 2008 with a shoulder injury and the world number three looked determined to make up for lost time as she reached the second round for the loss of just two games.
The 25-year-old, who carried her country's flag at the Games' spectacular opening ceremony at the Olympic Park on Friday, will play Britain's Laura Robson or Lucie Safarova of the Czech Republic for a last 16 berth.
"It was incredible to finally start the Olympics," Sharapova said. "I've certainly been waiting for this moment since I was a little girl so it was nice to get a win in my first Olympic match.
"It took many years to get here so it's pretty special. It was a big moment for me."
Fourth seedprogressed in between the showers on Court Two, the Spaniard beating Canada's Vasek Pospisil 6-4, 6-4, while French fifth seed Jo-Wilfried Tsonga, twice a Wimbledon semi-finalist, had to dig deep before defeating Brazil's Thomaz Bellucci 6-7 (5/7), 6-4, 6-4 under the roof.
Meanwhile, world number two Agnieszka Radwanska endured more Centre Court woe as the Polish second seed was beaten 7-5, 6-7 (5/7), 6-4 by Germany's Julia Goerges, less than a month after her Wimbledon final defeat to Serena Williams.
Despite the heavy rain, tournament organisers are confident the weather won't disrupt the schedule.
"There's no reason to panic. The first two rounds are spread over two days each so there's plenty of time to catch up," venue media manager John Dolan told AFP.