Resuming day four with an overnight lead of 67, Dinesh Chandimal and Ramesh Mendis went about their business in the first hour, again frustrating the Australians.
Emerging spinner Mehidy Hasan Miraz was the hero for Bangladesh with a brilliant spell that netted 3/36 and the 24-year-old was adjudged as the Player of the Match.
Serbia's Novak Djokovic went past Roger Federer's tally of 20 grand slam titles, clinching his 21st grand slam title after defeating Australia's Nick Kyrgios in the Wimbledon men's singles final on Sunday.