Michael Clarke (93) and the returning Mike Hussey (54) bailed their team out of trouble to help set up a daunting 324-6 but Kenya defied the much-vaunted Australian fast bowling unit to score a respectable 264-6 in Group A.
Earlier, opener Brad Haddin had made 65 but Australia found themselves under unexpected pressure at one stage at 143-4.
After four straight losses, Kenya had clearly decided not to go down without a fight and Tanmay Mishra (72) along with Collins Obuya (98 not out) resisted with a stubborn stand of 115 for the fourth wicket.
The pace trio of Brett Lee, Shaun Tait and Mitchell Johnson regularly generated speeds in excess of 140 kmph but the Kenyan batsmen gave as good as they got and notched up their highest score in the tournament so far.
Three of the six Kenyan wickets to fall were by run-outs as the Australian fast bowlers and spinners almost ran out of ideas to dismiss a batting side which was skittled out in their previous four matches.
It had seemed as if the match was headed for a fast finish as Kenya slumped to 46-3 in the 10th over. But as the pitch lost its pace, Mishra took on the role of the aggressor and clobbered eight boundaries and one huge six.
Obuya, however, was more restrained at the start of his innings but accelerated towards the end and singled out Shane Watson for some especially harsh treatment.
Thomas Odoyo joined the African party with a 38-ball 35 at the end but the Kenyans always were well behind the asking run-rate and their valiant attempt fell short.
Earlier, Clarke (93 off 80 balls) paced his innings to perfection to avoid a middle-order collapse after Australia lost three quick wickets in the space of 15 balls at the end of the
27th over.
Clarke and Hussey (54 in 43 balls), who celebrated his return to the World Cup squad with a typically industrious innings, came together with Australia in a spot of bother and with a 300 plus score looking a long way off.
They immediately put the Kenyan fielders under pressure with singles and twos and the odd boundary to wrest the initiative back with a 114-run partnership for the fifth wicket at better than a run a ball.
Shane Watson (21) and captain Ricky Ponting (36) also got some runs under their belt.
