The left-handed opener contained his natural aggressive self before swinging his arms freely to build a 166-run knock, which steered Australia to a mammoth 381 for five, their second highest score in World Cup.
Warner, who had hit a hundred against Pakistan as well, added 121 runs with his skipper Aaron Finch (53) in a risk-free opening partnership and then raised a 192-run stand with Usman Khawaja (89).
He completed his 16th ODI hundred, his sixth 150-plus knock, which came off 147 balls with 14 hits to fence and five over the ropes.
In reply, the 'Tigers', as expected, took the fight to the rival camp but ended up with 333 for eighth in stipulated overs.
Mushfiqur Rahim (102 not out), Mahmudullah (69), Tamim Iqbal (62) and in-form Shakib Al Hasan (41) gave their all in the chase but the effort still proved insufficient though the total was their best ever in ODIs.
It was Rahim's first hundred in a World Cup game and seventh overall.
Paceman Mitchell Starc (2/55) and Nathan Coulter-Nile (2/58) shared four wickets between them.
The win took Australia to top of the table with 10 points from six games while Bangladesh remained at number five with five points and now need to win their remaining three games.
Earlier, medium pacer Soumya Sarkar (3/58) took three wickets while Mutsafizur Rehman (1/69) accounted for one Australian batsman.
Mashrafe Mortaza and Rehman largely remained disciplined in their opening spells, bowling wicket-to-wicket. Warner and Finch also preferred playing the risk-free game and did not attack much, managing an under-six run-rate.
It was only after spinners -- Shakib and Mehidy Hasan -- were introduced that the two batsmen showed some aggression. Warner launched one from Shakib for a massive six over mid-wicket while Finch punished Hasan with back-to-back shots over the ropes.