The West Indies smashed the target of 180 with five balls in hand, taking a 1-0 lead in the three-match series.
"It's always important when you come to Sri Lanka to take an early lead, we know that Sri Lanka is a team that play excellent cricket at home," said West Indies skipper Rovman Powell.
He said it was key to "throw the first punch", and then, "once you get on top, you try to stay on top for as long as possible."
The run chase began with fireworks, as the duo of King and Lewis amassed 74 runs within a six-over powerplay, putting Sri Lanka on the defensive.
King was the first to reach his half-century, elegantly carving a cover drive for four off Matheesha Pathirana.
His 50 came off just 25 balls, while Lewis followed shortly, needing only 27 deliveries for his half-century.
"My role was to get the team off to a good start - and it came off well," King said.
Together, King and Lewis added 107 runs in just nine overs for the opening wicket.
It was the highest partnership for West Indies against Sri Lanka in T20 cricket for any wicket.
The partnership was eventually broken when Pathirana deceived Lewis with a slower ball, the batsman edging it to Chamindu Wickramasinghe at backward point.
King went on to top-score with a blazing 63 off 33 balls, including 11 fours and a six.
With the openers setting up the chase, the middle order merely had to rotate the strike, picking singles and taking calculated risks to seal the win.
Sri Lanka attempted to claw back by picking up a few wickets, but the damage inflicted by the opening pair left the hosts in a near-impossible position.
All-rounder Roston Chase and captain Powell steadied the innings, contributing 32 runs for the fourth wicket.
Powell fell for 13 in the 17th over, mistiming a straight six attempt off Maheesh Theekshana to Wanindu Hasaranga at long-on.
Chase departed for 19, caught behind off Pathirana, but the job was nearly complete.
Despite torrential rain threatening to wash out play, the ground staff's swift efforts allowed the game to proceed after a 30-minute delay.
Earlier, half-centuries by Kamindu Mendis and Charith Asalanka had lifted Sri Lanka to a seemingly competitive 179, with the pair sharing an 82-run standoff 54 balls for the fourth wicket.
However, it proved insufficient against the explosive West Indian openers, who dismantled Sri Lanka's bowling attack.
"Whatever we did today it didn't work out for us, but we will come back after addressing a few issues," skipper Asalanka said.
"The plus point for us is that we are playing good cricket."
The West Indies are third in the global T20 rankings, while Sri Lanka languishes in eighth.
The remaining two T20s of the series, also at Dambulla, will be played on October 15th and 17th before the teams head to Pallekele for a three-match ODI series.
