Bhutan, who prop up the world rankings at number 209, are embarking on a maiden qualification campaign some three years before the tournament gets underway in Russia.
And Dorji struck in the 86th minute in Colombo after Sri Lanka had twice hit the woodwork to cap the momentous occasion with a 1-0 triumph in the first-leg encounter.
Brunei were also able to savour history. After 12 failed attempts, they finally got a win at the 13th attempt in World Cup qualifiers as Adi Said's 36th-minute was enough to sink Chinese Taipei 1-0.
Said's strike was Brunei's first in World Cup qualifiers in almost 30 years.
Thursday's action started with Timor-Leste routing Mongolia 4-1, while Cambodia were 3-0 victors over Macao.
The second leg of each tie will take place on Tuesday.
