Having dismissed Bangladesh for 227, the home side completed their chase with 79 balls to spare, following their five-wicket triumph on the same ground on Sunday.
King struck a fine 82 from 76 balls with eight fours and three sixes to register his seventh half-century in the format to add to his three centuries.
His innings was also a perfect early birthday gift ahead of the Jamaican turning 30 next Monday.
King shared an opening stand of 109 with Evin Lewis who made 49 from 62 deliveries with two fours and four sixes.
He then put on 66 with Keacy Carty before his innings was ended by a blistering yorker from promising young fast bowler Nahid Rana.
Carty made 45 before skipper Shai Hope (17) and Sherfane Rutherford (24) guided their side home on 230-3.
Rutherford wrapped up the win with a huge six off Shoriful Islam.
"We were clinical. We've been struggling to win series at home, but we hope to finish 3-0 now," said Hope who already has one eye on the 2027 World Cup after the West Indies failed to qualify for the 2023 tournament.
"Every game is important, we're trying to earn points and get up on the ladder to ensure we make the next ODI World Cup."
Earlier Seales took a career-best 4-22 from nine overs.
He sent back Soumya Sarkar, Litton Das and Mehidy Hasan Miraz to leave Bangladesh tottering on 54-3.
Opener Tanzid Hasan made a patient 46 before 38-year-old Mahmudullah, appearing in his 237th ODI, cracked 62 with two fours and four sixes before he became Seales's fourth victim.
Mahmudullah put on 92 with Tanzim Hasan Sakib (45) for the eighth wicket as Bangladesh pushed their total beyond the 200-mark.
"Our score wasn't enough, 300-plus was needed," admitted Bangladesh captain Mehidy.
"We bowled really well in the first ten overs but on this wicket, it's hard for bowlers to defend an under-par score."
The third and final match takes place at the same venue on Thursday before the two sides then meet in a three-game T20 series at Kingstown.
Brief scores
Bangladesh 227 all out in 45.5 overs (Mahmudullah 62, Tanzid Hasan 46, Tanzim Hasan Sakib 45; Jayden Seales 4-22) v West Indies 230-3 in 36.5 overs (Brandon King 82, Evin Lewis 49, Keacy Carty 45)
Result: West Indies won by seven wickets
Series: West Indies lead 2-0
Final match: Basseterre, Dec 12
