Renshaw survived nearly two sessions, facing 94 balls for his 45 runs while Australia lost five wickets, until he edged to Soumya Sarkar at slip.
Bangladesh was just one wicket away from victory when Soumya Sarkar took an excellent catch running backwards from slip after Nathan Lyon gloved Mehedi Hasan on the sweep, but Cummins provided some late drama.
David Warner hit 75 not out as Bangladesh's bid for a first ever Test triumph over Australia stalled on Tuesday.
Australia have called up spinner Steve O'Keefe to replace injured quick Josh Hazlewood for the second and final Test against Bangladesh.
The Australian middle order and lower-middle order succumbed to the pressure and gave in to Bangladesh spinners as they suffered a batting collapse. "Naturally they had aggression but we were aggressive too", said Mushfiqur.
Test cricket seems to have found its spark in the outcome of two different matches in which the dark horses showed remarkable resilience to defeat superior teams in matches where fortunes swung like a pendulum.
Taijul then dismissed Peter Handscomb for 15 and Ashton Agar for two while Shakib added the wicket of Matthew Wade (four) to his kitty.
Cabrera Suspended Seven Games, Sanchez And Wilson Four
Cabrera then shoved him in the chest and took a swing at the catcher with his left hand before being tackled by Romine. Detroit , however, have a losing record of 55 71, keeping them out of the playoff race for now.
"The Australian team were on the back foot, trying not to play an over".
Shakib sent back Warner and Smith, who made 37, in the morning session when Australia lost five wickets.
But when it came to matching the Aussies with respect to verbal volleys during this Test, Bangladesh were not far behind.
Defying all odds, Bangladesh registered its greatest win across all formats as they sealed their first Test win over Australia in what was one of the most thrilling five-day matches in recent times.
The loss of the hardiest of Australia's pace bowlers just a few months before they host England in an Ashes series around the New Year is a blow, however. The world's top-ranked Test all-rounder took 10 wickets for the match as well as making 84 in the first innings to earn man of the match honours. "They found out that we are no longer the Bangladesh of old, that we now have the players who can now change the course of a match from any position".
"We let ourselves down a bit in the first innings with the bat", Smith said. "It was pretty hard batting here in the second innings and I thought we did pretty well to get 240 in the end".