Malan and Morgan compiled a 51-run partnership to haul England back into the game after a career-best 3/19 spell for home spinner Tabraiz Shamsi had South Africa well placed to level the series.
The result also meant defending champions Mumbai Indians qualified for the play-offs.
Varun Chakravarthy claimed 5/20 as KKR won by 59 runs.
After the bowlers restricted KKR to 148/5, opener Quinton de Kock blazed his way to an unbeaten 78 off 44 balls to complete the task for Mumbai.
Chasing a modest target of 149, Mumbai were home and dry with 19 balls to spare.
Karthik handed over the reins to his deputy Morgan hours before their IPL match against Mumbai Indians.
Karthik told the KKR management that he wants to "focus on his batting and contributing more to the team's cause."
"Genuinely feel Eoin Morgan should lead the side, surely not DK. World Cup-winning captain should surely lead IPL side," Sreesanth tweeted after KKR suffered an 18-run defeat to Delhi Capitals on Saturday night.
England produced a brilliant comeback to beat Australia by two runs in Southampton.
Morgan blasted 66 from 33 balls to secure the win in what is the highest chase in any form of 20-over cricket at Old Trafford.