Collins Obuya (98 not out) fell agonizingly short of a century as he and Tanmay Mishra (72) led the resistance for Kenya, which finished on 264-6, its highest score of the tournament.
However, the Kenyans' scoring rate never really threatened Australia, which earlier posted a daunting 324-6 helped by a key innings from the returning Mike Hussey.
Hussey (54), who replaced his brother David in the side after joining the squad on Tuesday, and Michael Clarke (93) put on 114 runs for the fifth wicket after Kenya bowled tenaciously early on.
Australia, unbeaten in 33 World Cup matches and the only undefeated side in the tournament, has seven points from four games, one behind Group A leader New Zealand.
Kenya has lost all five matches so far, but at least restored pride with a battling effort in its penultimate game as Australia's bowlers toiled under the lights at the Chinnaswamy Stadium.
After winning its first two games comfortably, Australia had been kicking its heels for a week since its last game against Sri Lanka was abandoned after 33 overs, and with Kenya and Canada expected to provide mismatches, some supporters feared the four-time champions might be undercooked come the knockout stages.
Ricky Ponting had no hesitation in choosing to bat after winning the toss, eager to give his men valuable time in the middle ahead of Kenya's expected batting collapse, but Australia had to recover from a mid-innings wobble.
Nehemiah Odhiambo had opener Shane Watson caught behind on 21 early on and though Brad Haddin's steady 64 helped take Australia past the 100 mark for the loss of one wicket, his departure sparked the fall of three wickets in three overs.
Kenya went to the review system to dismiss Ponting after the Australian skipper was hit on the pad by Collins Obuya before Cameron White (2) was bowled by a Jimmy Kamande delivery which spun wickedly from wide of off stump.
As White looked openmouthed at his stumps, Kamande celebrated with a dance after seeing his side take three wickets for 16 runs and leave Australia on 143-4.
Cue the entrance of Hussey, who hit his first ball of the World Cup for four and, alongside Clarke, steadied any Australian nerves.
Clarke posted his second half-century of the tournament off 52 balls, and Hussey's 50 duly followed, his 34th in all and first at a World Cup, but he holed out to long-on three balls later to give Odhiambo his second wicket.
Clarke fell seven runs short of his sixth one-day century when he also found the man at long-on from Odhiambo's bowling, but his World Cup average still stands at an enviable 101.83 from 12 innings.
A crowd of 13,600 was inevitably behind the underdogs and opener Alex Obanda, making his World Cup debut, gave them something to cheer with two huge sixes as Kenya's reply began - the second hitting the roof of the stadium from Tait's bowling.
Tait had his revenge three balls later by clattering Obanda's stumps to leave Kenya teetering on 41-3, but the opener's audacity set the tone for a more than creditable batting display by Kenya.
A 25-run partnership between the Obuya brothers came to an end in calamitous fashion when Collins refused a quick single, leaving David completely stranded, but at least the younger brother stuck around with the impressive Mishra, who followed his 51 last time out against Canada with another fluid half-century against more testing opposition.
A concern for Australia might be the performance of spinners Steve Smith and Jason Krejza, who have still taken only three wickets between them in the tournament, leaving Ponting to rely heavily on his pace attack - although even that struggled against an obdurate Kenya.
Mishra eventually departed when he went for a dicey single, only for Obuya to again stay put, and Clarke's direct hit sent the frustrated batsman on his way.
The experienced Obuya, who had crept to 46 off 85 balls when Mishra departed, upped the pace and bludgeoned a six off Watson to complete his second World Cup half-century, but he could only manage a single off the last ball and was left stranded on 98 as Australia completed victory.
Australia now stays in Bangalore for its next game against Canada on Wednesday, while Kenya will play its final game in Kolkata against Zimbabwe in a week's time.
