There was a shock, though, at Eastbourne's Devonshire Park as defending champion Dominika Cibulkova suffered a second-round knockout by British player Heather Watson.
Watson, whose ranking has slumped to 126 in the world, delighted the home crowd with a 7-5 6-4 defeat of the fourth-seeded Slovakian.
Ostapenko, who shot up to 13th in the world after her stunning triumph in Paris, played with her usual mixture of clean winners and errors to overpower her opponent, despite a second set meltdown when her game misfired on the grass.
The 20-year-old Ostapenko, who got a first-round bye, will face either Britain's fifth-seeded Johanna Konta or Romanian Sorana Cirstea in round three.
World number nine Cibulkova saved three match points when Watson served at 5-3 in the second set but after breaking back she immediately dropped her own serve as her Wimbledon preparations were cut short.
Cibulkova has been bothered by a wrist injury this season but said that had not been a factor in her loss.
"It's more about to be more confident or to get some matches on my side, and it will be a different story," she told reporters. "Because right now it feels like the situations go against me in the match, and it just doesn't go my way."
There was also an early defeat for Canda's former Wimbledon runner-up Eugenie Bouchard who lost 6-3 3-6 6-2 to Czech Barbora Strycova.
(Reporting by Martyn Herman; Editing by Ken Ferris)
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