Ferrer, who last week beat Rafael Nadal at the Monte Carlo Masters, was easily beaten in straight sets by world number 55 Gabashvili.
The Russian got off to a great start by breaking Ferrer at the first time of asking but was then pegged back in the fifth game.
It looked like a tie-break might be needed but then Gabashvili broke to love to clinch the first set 6-4.
The second set had a similar feel as Gabashvili broke in the second game, but this time Ferrer had no answer and was broken again in the eighth game as Gabashvili wrapped up victory 6-4 6-2.
He will next face Spanish wildcard Inigo Cervantes in the third round.