The Proteas were set a target of 119 to win after a spin inspired bowling attack restricted England.
England pacer Jade Dernbach (2-31) sent an early scare through the South African top-order, but it failed to sway Kallis and Duminy who cruised toward the total with an over remaining.
Batting from start to finish, recalled all-rounder Kallis struck an unbeaten 48 from 44 balls, top scoring for South Africa, while Duminy chipped in with 47 from 54 balls.
On a pitch favouring the bowlers, Dernbach got England's defence off to an ideal start when he dismissed opener Richard Levi in the second over, edging to Graeme Swann at slip.
Faf du Plessis followed quickly in the next over when he was trapped LBW by Steven Finn as South Africa found themselves 14-2 with three overs played.
Dernbach's second wicket brought the game to life at 29 for three, when Proteas skipper AB de Villiers edged through to keeper Craig Kieswetter and departed for 10 from six balls.
Kallis then set in with Duminy to guide South Africa home.
Earlier, right arm off-spinner Johan Botha and Robin Peterson both claimed two wickets each.
Opener Kieswetter top scored with 25 from 24 balls, but there was little scoreboard impact from the English batsmen who were no match for the tourists.
Ravi Bopara could only manage six before he was caught at slip of the bowling of Dale Steyn (1-13 from four overs), while Eoin Morgan followed shortly when he was bowled by Botha on 10.
Kallis was superb in the field for the visitors, firstly running out Alex Hales for 11, then taking a superb diving catch to dismiss Samit Patel on four to have England at 85-7.
A late charge from captain Stuart Broad (18 not out) and Graeme Swann (17 not out) ensured England posted triple figures.
England and South Africa will meet again at Old Trafford on Monday in the second match of three.
- Jade Dernbach
- South Africa
- Graeme Swann