The unexpected coup was achieved after the mayor wrote to the director warning of 'a crisis' if the film was not shown in the town.
Mr Spielberg made an extra print available after Richard Goodridge wrote to tell him that local people, many of whom had postponed their summer holidays to see the film, were 'disappointed and angry' to hear that the small Welsh town's Lyric cinema would not be receiving one.
Later the film's distributors granted Carmarthen a preview on the same date as the official Royal premiere in central London which was attended by the Princess of Wales and a crowd of about 1,000 which had gathered outside to see the celebrities. The premiere was in aid of the Natural History Museum and the drugs charity Turning Point.
Mr Spielberg and Lord (Dickie) Attenborough, who stars in Jurassic Park as the scientist who re-creates Tyrannosaurus Rex and other dinosaurs from DNA - his first screen role for 13 years - joined a gaggle of other celebrities and Dr Jack Horner, the American palaeontologist and real-life model for the film.
British censors are allowing in children of any age, despite the sometimes gory scenes when dismembered limbs are strewn across the screen and a dinosaur eats a man alive. Mr Spielberg last night advised parents to view his film first if they were worried about the violence. 'Parents should make their own minds up,' he said.
All 740 Carmarthen tickets - pounds 2.50 for adults and half-price for children, compared with pounds 135 in the West End - were sold in less than an hour yesterday. Liz Evans, 47, the Lyric's director, who described the evening as 'the biggest event ever to hit Carmarthen', said yesterday: 'We are not going to let Leicester Square do it posher than us.'
She went on: 'We have bought our own inflatable dinosaurs for the foyer, the local museum has lent us its fossils and we have Jurassic cocktails - vodka, port and Cointreau - in the bar.
'All the staff will be in black tie tonight. You know nothing really happens west of Swansea so we are making the most of tonight. We are overjoyed. The only thing that would have made it better would be for the Princess of Wales to have seen it here rather than in London.'
The pounds 48m film followed the premiere of Dinas Neon, a bilingual Welsh/English musical written and performed by children from Fishguard High School.
Fourteen years ago, financial difficulties and the death of the owner forced the closure of the 1930s cinema. It fell into dereliction but Mrs Evans and other volunteers restored it. Jurassic Park, she said, would guarantee its future. 'It's been a real struggle to get this cinema back on its feet. At the beginning we even had to paint a screen with white emulsion and use 1930s projectors.'
Bill Hughes, 82, who was the Lyric's projectionist for 40 years before he retired last July, warned that the film would have to be 'a sell-out every night' of its month-long run to set a new audience record.
'We had nearly 27,000 come to see the film of the coronation of King George in 1937,' he said.
Town councillors dressed in official robes and chains for the opening. However, the guest of honour was 'devastated that he could not attend'. Mr Goodridge, a part-time postman, left the town before the premiere to represent Carmarthen in the Portuguese It's a Knockout competition.
Review of Jurassic Park: Adam Mars-Jones, page 16