Svitolina, who beat Iga Swiatek and Coco Gauff en route to the Italian Open title earlier this month, defeated world number 126 Kaitlin Quevedo 6-0, 6-4.
"It was a great match, I started very well in the first set," she said.
She struggled through her first-round tie, edging out Hungary's Anna Bondar in a deciding-set tie-break on Monday, before watching her husband Gael Monfils' final French Open match in the night session.
But Svitolina raced out of the blocks this time, quickly taking control against Quevedo.
The Spaniard competed better in the second set until a break in the ninth game helped Svitolina wrap up victory.
Svitolina, who reached her fourth career Slam semi-final earlier this year at the Australian Open, will next play Germany's Tamara Korpatsch, who made a major third round for the first time at the age of 31 by beating Chinese 32nd seed Wang Xinyu.
The Ukrainian seventh seed ended an eight-year wait for her fifth WTA 1000 trophy in Rome to underline her credentials as a contender in Paris.