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Basically the wand had never sworn allegiance to him:

1. Dumbledore owns the wand.
2. He was killed by Snape, so Voldemort thought the wand belonged to Snape.
3. Voldemort kills Snape, and assumes the wand is now his.

MEANWHILE:

1. Dumbledore owns the wand.
2. Draco Malfoy disarms Dumbledore and Dumbledore is thus defeated; the wand changes its allegiance to Malfoy.
3. Harry eventually disarms Draco and thus the elder wand belongs to him.

NOW:

1. The wand has aligned itself with Harry.
2. Voldemort casts the killing curse upon the part of his soul within Harry; that's what actually dies.
3. So Harry, still alive, is left in ownership of the elder wand.

The wand never belonged to Snape, and therefore never belonged to Voldemort. Elder is the wood most susceptible to yielding its ownership.