The Suns pulled clear late in the match to post a hard-fought 21.15 (141) to 13.11 (89) victory in front of 9317 fans at a sold-out Barossa Park on Saturday.
The Kangaroos led by eight points midway through the third quarter but conceded the next four goals before three-quarter time as Gold Coast flexed their muscles.
King had just six disposals but made most of them count as the game's leading goal-kicker.
Captain Noah Anderson (27 disposals, six clearances) and fellow midfield star Matt Rowell (26, 11) were influential, and Ben Long (three) was among the Suns' 14 individual goal-kickers.
It is the first time the Suns have started a season with four consecutive wins, after entering the AFL in 2011.
They will equal a club record of five consecutive victories - set in 2014 - if they beat coach Damien Hardwick's former club Richmond at Marvel Stadium next week.
North Melbourne (1-4) have now lost three straight games ahead of a clash with Carlton on Good Friday.
Fresh off signing a massive new seven-year contract, Luke Davies-Uniacke was the Kangaroos' best with 26 disposals and eight clearances.
Caleb Daniel (32 disposals) and Harry Sheezel (27 touches, one goal) were also busy, while key forwards Nick Larkey and Jack Darling (two each) were among the multiple goal-kickers.
Gold Coast led by as much as 25 points in the second quarter but were pegged back and led by just eight at the main break.
The Kangaroos hit the front for the first time when they kicked the first three goals of the second half.
But the Suns kicked the next four majors without reply before three-quarter time, seizing momentum with a Rowell snap on the siren.
Jake Rogers kicked the first of the final term to give Gold Coast a handy buffer and they were never challenged after that.
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