How did Eliezer save his father even after his father had been sent "to the left?"
I believe that some clarification might be needed in this particular analysis. Initially, it should be noted that Eliezer doesn't really "save" his father. In one of the most emotionally brutal portions of the narrative, Wiesel shows that life and death in the Holocaust were determined with random and arbitrary condition. It is this reality in which Eliezer and his father are sent "to the left:"
"Men to the left! Women to the right!" Eight words spoken quietly, indifferently, without emotion. Eight simple, short words. Yet that was the moment when I left my mother. There was no time to think, and I already felt my father's hand press against mine: we were alone. In a fraction of a second I could see my mother, my sisters, move to the right. Tzipora was holding Mother's hand. I saw them walking farther and farther away; Mother was stroking my sister's blond hair, as if to protect her. And I walked on with my father, with the men. I didn't know that this was the moment in time and the place where I was leaving my mother and Tzipora forever. I kept walking, my father holding my hand.
As they move, Eliezer and his father hear the words of other prisoners. They tell both men to lie about their age. Eliezer does not know if these prisoners are helping father and son, but he does as they say. Wiesel describes how the words almost come from another source, reflecting the beginning of alienation that Eliezer experiences.
At this moment, Wiesel shows how there is not really a moment in which Eliezer saves his father. The words of the SS officer determine life and death with an almost callous indifference to human dignity. The words are spoken without emotion. Words that indicate who will live and who will die are given as dispassionate orders to be followed, items on a list to be done and crossed off. The traditional narrative would be almost heroic in which one saves another. Yet, there is little of that in what Wiesel renders. Eliezer's father is holding his son's hand and walking in the line where death is not instantaneous. This moment is transformative because it is the first time where Eliezer learns about the fragile condition of life in the camps. It is also reflective of how Eliezer recognizes that there is little in way of order and structure that governs life during the Holocaust.
For those who were victimized by the Nazis, heroism gives way to the struggle for survival. Eliezer walks on with his father, unaware that they will not see the women in their lives again. Eliezer walks with his father because he knows no other path. It is in this where both are saved. Yet, they are more spared death for the moment. There is no real sense of heroism in terms of one saving the other. The impersonal command of "to the left" temporarily staves off death for Eliezer and his father. However, its presence is looming and something that serves to alienate Eliezer throughout the narrative from his father, his people, his God, and from himself.