Chasing just 141 for victory, the hosts reached their target in the 22nd over, Gibbs finishing undefeated on 87 with his partner Gary Kirsten on a more sedate 52.
It was a chastening exposure of the gulf in class between the two sides for the Kenyans, who never remotely threatened to cause an upset.
The result put South Africa's World Cup campaign back on track after their narrow loss to West Indies in the tournament's opening game.
Gibbs reached his fifty from 46 balls and then cut loose in search of a rapid victory in the knowledge that net run rates could prove significant in the World Cup's later stages.
He took 20 off Maurice Odumbe's second over to move from 55 to 75 and won the match with two further boundaries in what proved to be the final over. The right-hander's 87 came off 66 balls with 12 fours and four sixes and it was his 15th one-day half-century.
Kirsten looked supremely confident, facing 63 balls and hitting nine fours in his second fifty of the tournament.
Earlier, Lance Klusener confirmed his return to form with both bat and ball in a excellent spell of bowling to wrap up the Kenyan innings in the 38th over.
After his batting heroics had come so close to taking South Africa to an improbable win over West Indies on Sunday, Klusener's form with the ball against the Kenyans confirmed that he remains a potent force despite a poor run coming into the World Cup.
Klusener's wickets all came late in the innings as the Kenyans struggled to consolidate after a rocky start.
The trouble began early for Kenya and was self-inflicted, Gibbs swooping from cover to throw down the stumps and run out opener Kennedy Otieno (one) at the non-striker's end.
When Brijal Patel edged Shaun Pollock to wicketkeeper Mark Boucher to depart for one in the next over, Kenya were seven for two.
Wickets continued to fall at regular intervals with only Ravindhu Shah mounting any prolonged resistance, the Kenyan opener cracking four boundaries off Jacques Kallis in a three-over spell that cost 23 runs.
He reached his ninth one-day fifty before being run out by an accurate throw from the square leg boundary by Klusener, his 60 coming off 87 balls and including seven fours.
Klusener, who completed figures of four for 16 from eight tidy overs, swiftly finished off the innings, and the only concern for South Africa was the number of chances they missed in the field.
Boucher put down two catches and fumbled a stumping chance, while Pollock (twice) and Jonty Rhodes also spilled catches.
