Bangladesh will begin day three on 6-351, a first innings lead of 153, and with a chance to push their advantage above 200.
That will test Australia's battling top order when they try and set a decent chase for Bangladesh in the fourth innings.
"We have got some naturally aggressive batters all ready to move the scoreboard along. Hopefully the wicket stays true and nice and we can put some pressure back on their bowlers," Webster said.
"There is still three days of cricket left and a day and half of really good batting at a half-decent clip gets us right back in this contest.
"Batting last in a Test match on a hopefully worn wicket could be tricky (for Bangladesh) if it is a small chase.
"I think that is our obvious way to win the game."
Two backs against-the-wall victories in the past, orchestrated by Michael Hussey and Shane Warne, provide a glimpse into the kind of heroics that will be necessary.
In 2010 in Sydney the Australian side overcame their biggest first innings deficit to win a home Test when they trailed Pakistan by 206 runs. Hussey made a brilliant unbeaten 134 in the second innings to set up a tricky target of 176 for Pakistan and Nathan Hauritz (5-53) spun Australia to a famous 36-run win.
In Colombo in 1992 Australia pulled off what Allan Border called "the biggest heist since the Great Train Robbery" when they trailed Sri Lanka by 291 on the first innings. Every Australian batter reached double figures in the second innings tally of 471.
Sri Lanka needed just 181 runs to win and Border threw the ball to rookie Warne who took 3-11 in 5.1 overs at the death to clean up the tail and secure a 16-run win. Warne never looked back from that moment.
What those two wins show is that it will take special acts by individuals and a great team performance for Australia to beat Bangladesh from where they are situated at the end of day two.Â
Veteran spinner Nathan Lyon was played well by Bangladesh's batters on day two but he will be crucial on the fourth or fifth day.
The batters will hold the key to setting up a tally to defend with Jake Weatherald, Marnus Labuschagne and Cameron Green all in need of big scores.
Webster said the team was up for the challenge.
"Our batting group was disappointing on day one so we are going to have to put our hand up and bat long periods like they did," he said.
"The way we are going to win it is late on day five and I am sure we are going to be up for the contest.
"Obviously we have got to get these last four wickets as cheap as possible and put in two really good days of batting, which is going to be hard work no doubt, but the boys in the dressing room have full faith that we have the calibre to do it."
