Palmer, who worked for business-to-business publishing firm ITP, and Acors, of Bromley, south-east London, were also fined 1,000 dirham (around £160) and will be deported after serving their sentences in a Dubai prison.
The pair were arrested , just hours after meeting at a champagne brunch at Dubai's Le Meridien hotel.
A police officer told the court he had warned them about their inappropriate behaviour, but returned later to find them having sex on a sun lounger.
They denied the charges of public indecency and having unmarried sex, with Palmer, of Oakham, Rutland, claiming they were "just kissing and hugging".
Judge Hamdi Abul Kharr of Dubai's Court of First Instance handed down the sentences in the pair's absence.
Their defence lawyer Hassan Matter said he would be appealing the verdict. He has 15 days to appeal.
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