Garbine, a three-time Rome semi-finalist, was slated to face last week's Madrid semi-finalist Anastasia Pavlyuchenkova on Tuesday, but the Russian withdrew due to an abdominal injury.
In another first-round match, before rain suspended day's play proceedings, Russia's Veronika Kudermetova notched a hard-fought 4-6, 6-2, 6-3 win over Belgium's world No.14 Elise Mertens in windy conditions.
Garbine won nearly 80 per cent of points returning Patricia's first serve and converted six of her eight break points to romp to victory. Garbine had 20 winners to 11 unforced errors while Patricia was undone by 24 unforced errors.
After an early exchange of breaks, Garbine surged ahead 4-1, keeping pressure on Patricia with her smothering groundstrokes. The Spaniard used a deep return to break the Romanian again for 5-1 before wrapping up the set.
In the second set, Patricia fell behind 0-2, but the Romanian pulled back to level 2-2. Then, as the rain came down harder, Garbine got more determined, cracking a series of big returns to break Patricia at love and reclaim her advantage at 3-2.
Elise had defeated Veronika in straight sets in each of their three previous meetings at the Tour level. But the world No.28 at last claimed a victory over Elise as she fought back from a set down to triumph in two hours and 19 minutes and claim a spot in the second round.