An unbeaten century from Darren Lehmann put Australia in firm control of the second Test against Bangladesh on Saturday.

Lehmann's second century in two innings against the visitors helped a dominant Australia to reach 351 for three, 56 runs ahead of Bangladesh, at the close of the second day.

Resuming on their overnight score of 289 for eight, Bangladesh lasted just 13 balls for the addition of six runs as Jason Gillespie (3-57) and Glenn McGrath (1-57) dismissed tailenders Mashrafe Mortaza for eight and Tapash Baisya for 25.

Lehmann, who hit 18 boundaries in his 156 not out, shared an unbroken fourth wicket partnership of 219 with captain Steve Waugh.

Australia had lost Justin Langer for one with the score on 14 before Matthew Hayden (50) and Ricky Ponting (59) put on 91 for the second wicket.

Off-spinner Sanwar Hossain (2-87) claimed the two wickets to fall in the afternoon session before Lehmann and Waugh -- who both scored centuries in the first Test -- restored order to the Australian innings.

Waugh's 74 not out kept him on course for his 32nd Test century.

Saturday's effort continued left-hander Lehmann's resurgence as the 33-year-old hit his third century in five Tests.

Sent in to bat by Australia, Bangladesh's 295 was their highest first innings total since their 400 on Test debut against India in Dhaka three years ago.

Leg-spinner Stuart MacGill took 5-77 for Australia after the pace attack had struggled to break through the top order.

Top-ranked Australia lead the two-match series 1-0 after Bangladesh, who have not won a Test in 20 attempts, lost the first Test inside three days by an innings and 132 runs in Darwin last week.