It's hard to know what meets your standards for "3D paintings," but the Faiyum (or Fayum) Funeral Portraits of the first through third century might be candidates: here's an example of a particularly famous and successful one, with some helpful explanatory text. These lasted for so long because they were done with encaustic paint, which is basically made of wax with pigment mixed in, and is, as you can see, extremely durable. Many paintings of the ancient world, made of more ephemeral materials, have not survived.

A little bit more background on these paintings, which came from what is known as Roman Egypt:

"After the battle of Actium and the death of Cleopatra VII (30 B.C.), Egypt became part of the Roman Empire.

...

"The truly multicultural population, especially in the cities of Roman Egypt, provided a fertile ground for phenomena such as the painted panel portraits on mummies. In their artistic style and technique, the portraits on wood panels followed the Greek painting tradition of depicting the subject in three-quarter view, with a single light source casting realistic shadows and highlights on the face. Indeed, since practically no panel paintings from the Greek world have been preserved, the mummy portraits — conserved by Egypt's arid climate — are the only examples of an art form that ancient literary sources place among the highest achievements of Greek culture."