Sociedad coach Arrasate has come under pressure following his team's poor start to the season, which had seen them win just one of their seven La Liga matches - against Real Madrid - prior to Getafe's visit to San Sebastian.
The 36-year-old was backed by Sociedad president Jokin Aperribay before the international break and looked set to be boosted by a welcome victory when substitute Pablo Hervias put the hosts ahead with eight minutes remaining.
However, Yoda equalised in the last minute of normal time with his maiden goal for Getafe and then grabbed a dramatic winner following superb work from Sammir, who rounded off a superb run by squaring for his team-mate to convert.
Getafe were therefore able to celebrate their first top-flight victory at the Estadio Anoeta, while Sociedad remain a point ahead of bottom club Cordoba.
Hervais appeared likely to be the home hero when he popped up at the far post to apply the finishing touch to a superb move.
Sergio Canales, another second-half replacement for Sociedad, produced a cheeky backheel into the path of Carlos Vela following a quickly taken throw-in and the latter picked out Hervias with a clever cross using the outside of his left boot.
But Arrasate's men were dealt a painful blow when Yoda levelled with a low left-footed shot from the edge of the area, seconds after seeing a similar effort charged down.
Remarkably, there was further misery to come for Sociedad as Sammir burst down the left wing and dribbled to the byline before picking out Yoda, who made no mistake with the goal at his mercy.
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