Tshering Dorji scored the only goal of the match in the 84th minute for the small Himalayan nation, ranked last of the 209 teams in FIFA's rankings, in steamy Colombo.
"It's a very happy moment for my life. It was moment that I have been waiting for...it was a precious moment to score, and it was a perfect moment to score the goal," Dorji told reporters.
Before Thursday, Bhutan had only three wins to their name and were beaten 5-2 by Sri Lanka in their last international match at the 2013 South Asian Football Championships in Kathmandu.
The performance from the side, who were once thrashed 20-0 by Kuwait in an Asian Cup qualifier in 2000, drew praise from even FIFA president Sepp Blatter who described it as "a wonderful, historic moment" on Twitter.
Sri Lanka's head coach Nikola Kavazovic said his team paid for taking Bhutan lightly but was confident they could overturn the deficit in the return leg on Tuesday.
"They were a better team and they deserve to win," said the Serbian. "We thought the Bhutani team (was) going to be easy but the things were totally different on the field.
"I'm still convinced that we are going to win the second stage."
Brunei also won for the first time in the qualifiers, beating higher-ranked Taiwan with a 36th-minute goal from Adi Said while Cambodia defeated Macau 3-0 in Phnom Penh.
Lowly East Timor earlier kicked off the road to Russia 2018 by registering their first ever World Cup qualifying win, a 4-1 success over Mongolia in Dili.
Striker Chiquito Filipe do Carmo scored the first goals of a campaign that will see all of FIFA's 209 members play more than 800 matches to determine which 31 sides will join the hosts at the finals.
The victory was only the fourth the 185th-ranked East Timor achieved since becoming FIFA members in 2005.
Such was the excitement in the Portuguese-speaking Southeast Asian nation, that a big screen was erected outside the Municipal Stadium for fans who couldn't get their hands on one of the 10,000 tickets on sale.
India moved closer to the next round with a 2-0 win at home against Nepal.
Both goals came in the second half through India's top international scorer Sunil Chhetri, who also missed a penalty and the chance to complete his hat-trick.
Yemen host Pakistan, ranked highest at 170 among the 12 lesser-ranked Asian teams in the first round, in the last match of the day.
The six aggregate winners will move into the second round of the Asian World Cup campaign, which doubles as the qualifiers for the 24-team 2019 Asian Cup, where the likes of regional powerhouses Japan, Australia and Iran enter the fold.
(Writing by Patrick Johnston in Singapore and Sudipto Ganguly in Mumbai)
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