The hosts regrouped through Shakib Al Hasan and Tamim Iqbal, who put on a 155-run fourth-wicket stand, but there was no doubting the importance of Cummins' early blitz.
Both players have regularly appeared in limited overs matches against Australia, and Shakib has played in the Big Bash League, however the passing Australian fan could understandably have been relatively unfamiliar with the pair.
Even though Australia were reduced to 18 for three in reply to 260, Lyon did not think Bangladesh were running away with the game. Agar will partner with offie Nathan Lyon on a supposedly spin friendly wicket.
Spinner Mededi Hasan Miraz - who destroyed England late a year ago - ensured David Warner's poor record on the subcontinent continued, removing the Australian vice-captain LBW for eight.
A third batsman was run out, leaving Australia precariously placed on 18-3 at stumps.
Australia squad: Steve Smith (c), David Warner (vc), Ashton Agar, Jackson Bird, Hilton Cartwright, Pat Cummins, Peter Handscomb, Josh Hazlewood, Usman Khawaja, Nathan Lyon, Glenn Maxwell, Matthew Renshaw, Mitchell Swepson, Matthew Wade.
But there was redemption for Bangladesh - meeting Australia in a Test for the first time in over a decade - when their spinners took two scalps in the final moments of the session. Though by no means as freakish as Warne nor an all-round talent in the class of Richie Benaud, the bowler-batsman-captain whose 248-wicket tally he passed on day one in Dhaka, Lyon never gives anything less than his most unsparing effort.
Tamim, who is Bangladesh's highest scorer in both Test and ODIs, showed he belongs in a class of his own as he did not lose his composure while seeing off the pacers during the crucial early period.
"He's probably copped a bit from his Asian series where he hasn't taken those massive amounts of wickets", Starc said.
Australia's most recent trips to the subcontinent ended in defeat. We still lost two Test matches.
The 250th wicket, a skidder that trapped Taijul Islam, demonstrated one of the ways in which Lyon has grown.
Recalled left-arm spinner Agar chipped in late to finish with three wickets in his first Test since 2013.
"I think our spin attack is better than theirs".
"We have seen them do it before in Sri Lanka and India". There was more damage in Cummins' next over as the quick found an inside edge to remove Imrul Kayes caught behind for a duck.
Usman Khawaja - whose return to the Test side has started horrendously - was caught short of his ground after pursuing a mindless single, adding to the early-innings woes of the tourists.