Tshering Dorji scored the only goal in the 81st minute at Colombo's Sugathadasa stadium, stunning the vast majority of the 3,500-strong crowd who had been expecting the hosts to swat aside the visitors.
The winner came as Bhutan launched a counter attack after a sustained period of Sri Lankan pressure, with the skipper Karma Shedrup Tshering passing to Dorji who slotted home calmly from inside the penalty box.
But Bhutan, who normally play against a backdrop of snowy Himalayan peaks, reaped the benefits of acclimatising in the build-up at a training camp in Thailand and coped well with the humid conditions.
"We tried hard to acclimatise to the conditions here. We didn't allow humidity to become a problem," a delighted Bhutan coach Chokey Nima said after what was the country's first ever appearance in the World Cup.
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The two teams meet again when Sri Lanka travel to Bhutan's capital Thimpu for a return match on March 17.
Bhutan has been a member of FIFA only since 2000 and a lack of funding had prevented it from taking part in previous World Cup qualification tournaments.
Today's match was one a group featuring the 12 lowest-ranked teams in the Asian confederation who were kicking off the marathon contest for the right to take part in the 2018 World Cup finals in Russia.