Connacht moved into the play-off positions in Conference A as they opened their South African tour with a bonus-point victory in Port Elizabeth.
The westerners' pack were dominant, while their scrum battered Kings and earned a vital penalty try in the opening half.
Their fifth win of the season lifts Connacht above Ospreys and Cardiff Blues in the standings.
The Southern Kings showed flashes of brilliance, including their two tries from Masixole Banda and Ntabeni Dukisa.
Jack Carty landed a penalty after four minutes, and six minutes later, his kick picked out Cian Kelleher for the opening try. Carty converted.
However, a penalty won at the lineout allowed Kings to enter the visitors' 22, and Banda skipped tackles to score.
Connacht held the upper hand as referee George Clancy doled out the penalties against Kings - eventually loosehead Luphumlo Mguca was sin-binned - and one more scrum penalty saw the penalty try awarded.
Connacht struck again before the break, Matt Healy going over. Carty converted to make it 24-7 at half-time.
Kings improved after the break. The arrival of Dries van Schalkwyk helped, and he was involved in their second try, a wonderful team score, finished off by Dukisa.
But Connacht bagged their fourth try just after the hour mark, replacement Paul Boyle getting a fine score under the posts.
Southern Kings - M Banda; M Makase, H Klaasen (T Kruger 64), B Klaasen, Y Penxe; M Du Toit (N Dukisa h-t), S Ungerer (G Masimla 63); L Mguca (A Tshakweni 56), A Van Rooyen (T Balekile 57), N Oosthuizen (L Pupuma 63); S Greeff (A Van Schalkwyk 41-51 HIA, 59), JC Astle (c); CJ Velleman, J Van Vuuren (A Tshakweni 36-45) (M Burger 59), R Lerm.
Connacht - T O'Halloran (D Leader 72); C Kelleher, K Godwin, T Farrell, M Healy; J Carty (D Horwitz 60), C Blade (J Mitchell 63); D Buckley (P McCabe h-t), S Delahunt (T McCartney 53), C Carey (D Robertson McCoy 51); U Dillane, J Cannon (G Thornbury 60); S O'Brien (P Boyle 41), C Fainga'a, J Butler (c).
REF - G Clancy (IRFU)