In 1956, the Soviet Union having passed from Stalinist terror to Khrushchevian unease, the state cinema industry produced one of the most commercially successful films in its history: a musical comedy called Carnival Night, the debut feature from Eldar Ryazanov, previously a documentary-maker.

It is as light and nimble as a racehorse jockey – a little miracle of innocence, gaiety, mischief and fun, proof that Soviet cinema could do musicals to be compared to Hollywood’s MGM greats, in spirit, if not exactly in budget. Ryazanov went on to be renowned for slyly satirising the grisliness of apparatchiks and officials, and Carnival Night is surely an influence on Miloš Forman’s The Firemen’s Ball.

The star is veteran Russian comic actor Igor Ilyinsky, who plays the pompous Comrade Ogurtsov, a blustering stuffed shirt and humourless party placeman who has suddenly been put in charge of the New Year’s Eve party at the House of Culture.

To the dismay of everyone working on the entertainment, killjoy Ogurtsov tells everyone that the modern jazz band should be replaced with older musicians performing the Soviet-approved syrupy emotional music, and the carnivalesque master of ceremonies should be a state functionary reading an educational lecture. He watches the clowns Tip and Top rehearse their routine and demands they do something more respectable and less licentious, and that they use their full names. He also tells the ballerina that her tutu is too revealing: “Naked legs will not educate our audience.”

But two of the organisers plot to stop this misery merchant spoiling their fun: Lena, played by Lyudmila Gurchenko, who in a wasp-waisted outfit performs the evening’s showstopping number, and Grisha (Yuri Belov), the assistant director, who is shyly in love with her.

The action barrels along with terrific sprightliness and flair and Ilyinsky himself is a joy: he pretends to be an aficionado of Shakespeare (and is perhaps inspired by Dogberry from Much Ado About Nothing or Malvolio from Twelfth Night), and it is an inspired piece of comedy business when he comes out on stage to make some grumpily puritan announcement only to find that the conjuror has planted all sorts of things in his pockets, including two doves. He is incidentally eerily similar to the British comedy actor Edward Chapman, who played the same grumpy bank-manager sort of roles in this period. This is a pre-Christmas treat.

Showing before it at London’s ICA is the Russian cinema foundation Kino Klassika’s restored version of Sergei Parajanov’s wordless 10-minute film Hakob Hovnatanyan from 1967, a visual and thematic precursor to his rhapsodic masterpiece The Colour of Pomegranates. The Georgian-born Armenian director shot it after completing the script and screen tests for Pomegranates, but before principal photography began.

Hakob Hovnatanyan is a study of the titular 19th-century Armenian artist, the so-called Raphael of Tiflis, who was descended from a distinguished lineage of artists and became himself a brilliantly accomplished portraitist, and it is also a homage to the city of Tiflis, or Tbilisi, itself. Parajanov’s film is a juxtaposition of images that is not really a documentary in the conventional sense, but more a cine-diorama, a succession of ideas and figures, encased and preserved within the screen – not far from the collages and assemblages that he created as an artist. It is a kind of dramatised art history – Parajanov wanted to convey the “folk vision” of art without the “museum greasepaint”, and this is his way of doing it.

We see the portraits themselves, with close-ups on detail, but the film is also a deconstruction of portraiture, in that it shows its ambient circumstance around painting: laces, playing cards, carpets, Bibles, rosaries, a piano. These are objects fetishised for their connection with the past. We hear chatter in French, the refined language of the upper classes. It is clearly not merely Russian influence being brought to bear on Armenia but also the material culture of the west.

A young couple appear to go on a carriage ride. We see and hear a barrel organ playing in the street. The carriage arrives in the Armenian Pantheon in Tbilisi, where modernity is represented by power lines and a cable car, but the ancient verities of religion with its nationalist implications are shown in the domes of a Russian Orthodox church, and also the 13th-century Georgian church of Metekhi, on which the film closes, and an equestrian statue of Vakhtang Gorgasali, the sixth-century monarch who was the founder of the city.

These iconic symbols trace a complex pattern of myths and memories: an assertion of national identity that the government might well have found subtly, or not so subtly, subversive. But as with The Colour of Pomegranates, there is something akin to iconography and religious observance that Parajanov has alchemised into a secular mystery of art.

• Peter Bradshaw is introducing a screening of Carnival Night and Hakob Hovnatanyan at the ICA, London, on 4 December.