Supayacetus is known from the holotype specimen MUSM 1465, a partial skeleton consisting of assorted remains including a badly weathered skull, various vertebrae and ribs, teeth as well as parts of the forelimbs and the sternum.

As Ocucajea, it was collected in the Archaeocete Valley site, located within the middle Eocene (40.4 to 37.2 million years ago) Paracas Formation of the Pisco Basin, Peru.

[1] The genus is named after Supay, the Incan god of death and ruler of the underworld, in combination with the suffix "cetus" ("ketos"), Ancient Greek for whale.

The ventral surface of the bulla is broadly divided into a lateral and a medial half by the median furrow, which spans about a third of the entire length of the bone.

[1][3] When described in 2011, the position of Supayacetus among basilosaurids was not well understood, with the original authors simply placing it within an unresolved Basilosauridae featuring it, Basilosaurus, Dorudon and Ocucajea.

Providing a more detailed phylogeny with a much greater number of taxa, they place Supayacetus as a very basal basilosaurid slightly less derived than Basilotritus (which some authors consider a synonym of Pachycetus).

Basilotritus Zygorhiza Chrysocetus Saghacetus Ancalecetus Cynthiacetus Basilosaurus Dorudon Ocucajea Kekenodontidae Neoceti A markedly different position was recovered by Antar and colleagues in 2023, whose work stands out for two reasons.

For one, their phylogenetic analysis weakly supports the idea that Supayacetus wasn't simply basal to Basilotritus/Pachycetus, but actually formed a monophyletic clade with the two then-recognized species and Antaecetus, which would place it in the family Pachycetinae.