Gibbs hit a robust 40-ball 72 coupled with Kallis's unbeaten 128 as South Africa's batsmen pulverised hapless Dutch bowling to muster 353-3 in a Group A match reduced to 40-over-a-side.
Ryan ten Doeschate then hit a fighting 57 as the Netherlands managed 132-9 in their 40 overs.
Doeschate shared a 42-run sixth wicket stand with Tim de Leede who made 21, in an otherwise dismal batting show by the Dutch.
Mark Boucher joined the run-feast with a rapid-fire 31-ball, unbeaten 75 which included nine boundaries and four sixes.
He also hit the fastest half-century in a World Cup match beating West Indian Brian Lara's 23-ball feat against Canada at Centurion in 2003 by two deliveries.
But it was Gibbs who grabbed the headlines.
He launched into Dutch right-arm leg-break bowler Daan van Bunge in the 30th over, hitting him for five straight sixes and one to deep mid-wicket at the Warner Park ground.
"It's up there with the best things I've done," said Gibbs.
"I never thought about getting six in a row, but if it's your day, it's your day.
"After the first three I thought I was in with a chance, but I decided I wasn't going to charge him, I'd wait to see what he does and luckily they fell into the right slot."
Kallis hit eleven boundaries and five sixes during his unbeaten 109-ball knock and added 115 runs for the third wicket with Gibbs off just 71 balls.
South Africa hit 18 sixes in all beating Pakistan's record of most sixes in a one-day innings of 14 hit against Sri Lanka at Nairobi in 1996-97.
The 33-year-old Gibbs followed West Indian great Sir Gary Sobers and India's Ravi Shastri who both hit six sixes in an over but they came in first class cricket.
Sobers was the first to reach the landmark playing for Nottinghamshire against Glamorgan at Swansea in 1968 with Malcolm Nash the bowler taking the punishment.
Former India all-rounder Ravi Shastri then equalled the feat playing for Bombay against Baroda in 1984.
Gibbs, playing his 199th match, finally holed out to van Bunge at long-on off Dutch captain Luuk van Troost in the 31st over much to the sigh of relief of some 500 orange-clad Dutch fans among a disappointing crowd of 3000.
He hit seven sixes and four boundaries during his entertaining innings.
Kallis, who watched Gibbs' onslaught at the other end, reached his 15th one-day hundred off 97 balls studded with ten boundaries and two sixes.
South African skipper Graeme Smith hit a 59-ball 67 with six boundaries and a six after his team had lost opener AB de Villiers, caught behind off the second ball of the innings to paceman Billy Stelling.
The historic feat will also cost a leading drinks firm one million dollars.
The Johnnie Walker company had already agreed to donate the money to charity in honour of the first player to register the landmark.
Gibbs also erased Sanath Jayasuriya's record of most runs in a one-day over which stood at 30 -- achieved twice against Pakistan's Aamir Sohail in Singapore in 1996 and New Zealander Chris Harris at Sharjah five years later.