Michael Clarke's 93 helped Australia overcome a mid-innings wobble as the champions made 324 for six against Kenya, eventually beating them by 60 runs in a World Cup Group A match on Sunday.
For Kenya, Collins Obuya made an unbeaten 98 after Tanmay Mishra had made an impressive 72 to stretch their fight against the world champions.
With this win, Australia's unbeaten streak at the World Cup has stretched to 33 matches dating back to 1999.
Vice-captain Clarke and the returning Michael Hussey (54), in for dropped younger brother David, shared a stand of 114 after Australia had lost three wickets for just 16 runs to be 143 for four.
Clarke, on the ground where he made a hundred on Test debut against India in 2004, took 52 balls over his first fifty with only three boundaries.
But he then cut loose before he holed out off fast bowler Nehemiah Odhiambo, who took three for 57.
Victory for Australia would see the title-holders, unbeaten in 32 matches at the World Cup dating back to 1999, into the quarter-finals.
Left-hander Hussey, playing his first match of the tournament after recovering from a hamstring problem and getting a late summons to the subcontinent as a replacement for injured fast bowler Doug Bollinger, once again demonstrated his coolness at the crease.
Odhiambo had opener Shane Watson (21) well caught by leaping wicket-keeper Maurice Ouma after Kenya lost the toss.
Next ball captain Ricky Ponting, walking across his stumps, survived an Odhiambo lbw appeal.
Opening batsman Brad Haddin, dropped twice off tough chances early in his innings, made 65 and helped Ponting add 89 for the second wicket.
Haddin completed his 50 off 63 balls with his eighth four, a late cut off Kenya captain Jimmy Kamande but going for a big hit off the same bowler he was caught at deep midwicket by Rakep Patel.
A score of 127 for two became 131-3 when Ponting was lbw on review to leg-spinner Collins Obuya for an unconvincing 36.
Kamande took two wickets for nine runs in eight balls with some sharply turning off-spinners on his way to two for 46.
But paceman Elijah Otieno's eight overs cost a colossal 75 runs.
Kenya's best total in four previous losing appearances at this tournament was the 198 they made in a five-wicket defeat by fellow non-Test nation Canada.
