Twenty-year-old Arruabarrena-Vecino broke the Russian's serve at the first chance but then threw away her service straight away to let Sharapova on board.
Sharapova then broke to move 4-3 ahead but she also let her opponent to break straight back before yet again snapping the Spaniard's serve to move 6-5 ahead.
This time she didn't waste the chance, converting the opener on the third set point.
The second was much simpler for the second seed as she started to find her groundstrokes, racing to victory with a 24-minute 6-0 set.
She will next face either Marion Bartoli or Sara Errani in California.