Interesting contrast between the traditional (set ca. 1979*):
О чем ты думаешь
and the spacy/disco-y setting of what WP says has a decent claim to being the first soviet music video, from the film "Soul", in 1981:
За тех, кто в море
and, hey, as long as we're watching something chock full of mylar, here's something (a bit less retro-cheesy) from Roscosmos about how to recover cosmonauts without a splashdown:
Как готовится посадка спускаемого аппарата