The stylish middle-order batsman, leading in his first one-day series after replacing Ricky Ponting as skipper last month, scored 101 for his sixth one-day hundred to help his team post a challenging 270/7 on a slow pitch.
Bangladesh never looked like achieving the target despite half-centuries from opener Tamim Iqbal (62) and skipper Shakib Al Hasan (51), finishing at 210/5. The Bangladeshi captain completed 3,000 one-day runs during his knock.
Mushfiqur Rahim (44 not out) and Mohammad Mahmudullah (28 not out) were the other notable contributors for Bangladesh, who now trail 1-0 in the three-match series. The last two one-dayers will be played in Dhaka on April 11 and 13.
Clarke, who cracked two sixes and six fours in his 111-ball knock, earlier propped up the innings just when Bangladesh looked like restricting Australia to a modest total with their tight spin bowling.
Australia, who lost to India in the World Cup quarterfinals, were struggling at 138/4 in the 30th over before the skipper added 84 runs for the fifth wicket with Michael Hussey (33).
Clarke, needing five runs off the last three deliveries of the innings to complete his hundred, smashed paceman Mashrafe Mortaza for a six over mid-wicket before being caught in the deep off the next ball.
Left-arm spinner Suhrawadi Shuvo, who dismissed Hussey and Steven Smith (one) in the same over, was the most successful bowler with 3-44.
Bangladesh, electing to field after winning the toss, struck in the fourth over when Mortaza, who missed the World Cup due to a knee injury, bowled Brad Haddin for 10.
Opener Shane Watson (37) and Ponting (34) then dominated the attack with attractive shots. The opener hit Mortaza for a four and a six off successive balls before lofting spinner Abdur Razzak over mid-wicket for a six.
Ponting also looked in excellent touch, cracking three successive fours off Mortaza and hoisting Shuvo over long-on for a six. His brilliant cameo ended when he was run out going for a third run.
Watson, who added 65 for the second wicket with Ponting, also fell when looking well set as he was trapped lbw by Razzak after hitting two sixes and three fours.
Brief scores
Australia 270 for 7 (Clarke 101, Shuvo 3-44)
Bangladesh 210 for 5 (Tamim 62, Shakib 51)
Results Australia won by 60 runs
