Svitolina, the fourth seed, received a first round bye and dropped just three games in a dominant 6-1 6-2 victory over 35th-ranked Petra Martic last night.
The 23-year-old Ukrainian won the biggest clay court title of her career last year at the Foro Italico. And she continued where she left off despite the rainy conditions, needing just over an hour to peg back her Croatian rival.
By contrast, Sharapova needed two and a half hours to master 18th-ranked Barty 7-5 3-6 6-2 in their first round match.
"It was tough, tough conditions," said 40th-ranked Sharapova, who reached the quarter-finals in Madrid last week. "It felt like I was playing three different matches.
"There was a long wait and the way the court played, the way she played, the shadows, the little bit of a breeze out there. So, a lot going on.
"I think it was a really good way to end the match, to get that win." Sharapova's victory, her 34th on clay in the Italian capital, came in her first meeting with Barty, who was making her Rome debut.
The game swung the Russian's direction in the final set when Sharapova held serve in a crucial 1-1 game from 0-40 down after having failed to convert three break points in the previous game.
Barty, ranked 18, saved two match points in the final game against the 2011, 2012 and 2015 winner but two unforced errors in a row handed Sharapova a second round berth.
"It's been a while since I played her, she's always been a tough opponent especially on clay," said the Russian of the Slovak who leads 2-1 in clay court meetings.
- Shapovalov shines again -
In the men's event, Belgian ninth seed David Goffin was given a scare after leading 5-1 in the first set before losing six games in a row and dropping the first set to home hope Marco Cecchinato.
The Masters Open finalist got back on track by winning the next two 6-2 6-2 to advance to the second round.
The 19-year-old will become the new Canadian number one next week in place of Milos Raonic.
"I'm a little bit in shock," he said. "It's crazy that it's come so early." After a sloppy start Shapovalov found his feet in the second set breaking for a 3-1 advantage after Berdych hit a forehand into the net.
The world number 29 clinched the set, on his third set point of a seven-minute game at 5-3, when Berdych netted a crosscourt backhand.
Berdych came within two points of victory in the ninth game, and Shapovalov raced to the first four points of the tie-break, holding on despite Berdych coming back dangerously for 5/5.
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