That was the first time I recall seeing a cinematic depiction of a face melting, but I'm wondering if some "master of horror" did it before 1981.
"Tales of Terror" (1963) starring Vincent Price. It was an anthology film consisting of three tales based on stories by Edgar Allan Poe, the third and final one was called The Facts in the Case of M. Valdemar and featured the character played by Vincent Price with a melting face. There are other movies I can think of with melting faces, The Terror, The Incredible Melting Man (1977?), etc. I think I will research this one and try to find one from an earlier film.
The Devils (1971) includes a graphic depiction of burning at the stake. When this cuts to the actor's face at various stages, there is clear burn damage in a fairly similar "melting" way. However it is not a continuous shot in the way that the scene in Raiders of the Lost Ark is.