Early tries from Colby Faing'a and Tiernan O'Halloran saw the visitors 14-0 up within ten minutes, before Peter Robb saw red for leading with a forearm.
Stefan Ungerer and Erich Cronjé’s brace got the hosts in contention in Port Elizabeth, but a resilient second-half performance saw Connacht take the victory, with Jack Carty scoring a crucial try after the break.
The writing looked to be on the wall within the first 60 seconds for the Kings, as Fainga'a profited from Ungerer’s fumble on halfway to run in unchallenged and get Connacht off to the perfect start.
And just five minutes later the visitors added their second, as some quick hands from Carty and Kyle Godwin on the Kings’ 22 allowed O'Halloran to break through, before sidestepping two defenders to touch down.
The game-changing moment came after 15 minutes in Port Elizabeth, as substitute Robb was adjudged to have connected with the neck of Howard Mnisi with his forearm, and was given his marching orders.
Things got even worse ten minutes later, as Godwin was shown yellow while trying to stop the unrelenting pressure on their try line, with Ungerer burrowing over from the ensuing penalty.
The hosts made the most of their time against 13 men, as Cronjé pierced the Connacht defence to level the scores three minutes later, before Carty slotted through a penalty to make it 17-14 to the visitors at the interval.
The Irish side came out after the break rejuvenated, and extended their lead through Carty as the fly-half crossed in the corner, while Cronjé went over for his second of the game on the hour mark to reduce the arrears back to three.
Connacht continued to dig deep in the last 20 minutes, with an outstanding effort at the scrum to force a penalty try to secure the bonus point, as the Kings struggled to break down the visitors' defence.