Garcia slid in to meet a Bryan Gil cross in the third minute, and he scored a similar goal to double his side's advantage early in the second half when he diverted home a cross from Edu Exposito.
The 31-year-old Garcia completed his treble in the 59th minute, picking the ball up near the byline before cutting inside and blasting it into the far corner from a tight angle.
Eibar, who hail from a town of under 30,000 inhabitants and have been in La Liga since 2014, had not won in the league since Jan. 3 and had lost their last five matches.
The victory, however, gave them a slither of hope of staying in the top flight.
They remained bottom of the table on 26 points, five behind Alaves who occupy the final place above the relegation zone with four games to go.