In a match between two players appearing in their first final, the 20-year-old Puig was on top from the start as she broke the Spaniard in her first service game. She also broke twice in the second set, including in the final game.
Puig dropped just nine points on serve all match, two of which were double-faults.
Puig next heads to the French Open where she has been drawn against 2010 finalist Sam Stosur.
Soler-Espinosa faces Chanelle Scheepers at Roland Garros.