Led by American important Jordan McRae and his game-high 30 points, United done enough to beat the Kings 105-101 in overtime at Margaret Court Arena in Melbourne.
Melbourne centre Daniel Kickert sunk a three-pointer with 9.8 seconds remaining to level the score 92-92 in the fourth quarter and Jason Cadee's floater sent the game into overtime after the Kings rallied from 13 points down in the third.
But Melbourne were not to be denied in the additional period, with the Kings - missing star recruit Josh Childress due to a hamstring injury - outscored 13-9 in overtime.
Kickert finished with 22 points for Melbourne, while Mark Worthington contributed 16 points and 10 rebounds in a double-double display for the home team.
The Kings - beaten for the first time since edging the third-placed Perth Wildcats 78-74 on Thursday - were led by captain Ben Magden (22) and Cadee (21), who combined for 43 points.
Melbourne are fourth in the standings, boasting a 9-7 win-loss record following their hard-fought 103-98 overtime victory at the Wollongong Hawks on Friday.
After surrendering a nine-point lead in the fourth term, McRae posted eight of his 30 points in overtime to help United to see off the cellar-dwelling Hawks at Win Entertainment Centre.
The New Zealand Breakers (12-5) remain the team to beat despite losing to the Cairns Taipans 83-59 on Sunday.
After toppling the Townsville Crocodiles 96-84 two days earlier, the Breakers were match for the Taipans (11-5), who outscored them in all four quarters at Cairns Convention Centre to jump up to second in the standings.
The win was a welcomed response for the Taipans after losing 90-86 against the lowly Adelaide 36ers on Friday.