Warner instantly reviewed Aleem Dar's decision but replays confirmed it was hitting middle and leg.
Just like in the first innings, when Australia were bowled all out for 217, Warner had to watch on as opening partner Matthew Renshaw departed early on to bring Usman Khawaja to the crease.
Shakib lived up to his billing as the world's number-one Test all-rounder, finishing with a match haul of 10 wickets and making 84 in Bangladesh's first-innings total of 260.
The day-four pitch ended up being relatively benign but the visitors still had no answers for the masterful Shakib, who time and again beat Australia's batsmen with turn and flight.
Resuming on 109-2, Warner batted with calculated aggression, while Smith was content to play second fiddle as they continued the good work they had started on Tuesday evening with some generous assistance from Lady Luck. Unbeaten on 75, he has scored almost 70 per cent of his team's runs and done it by blending attack and defence in equal measure.
"Shakib and Taijul bowled really well".More news: Yankees, Tigers Involved in Brawl; Miguel Cabrera, Austin Romine Ejected
Questions remain about whether the Australians were mentally prepared for their first series on Bangladeshi soil since 2006. Shakib & Tamim bhai were phenomenal! "We had that confidence and the belief came from the last two-three years". Mehedi claimed three for 62 including the prized scalp of skipper Steve Smith for eight.
"We were confident", Mushfiqur told reporters on Wednesday. But Shakib got the vital wickets of Warner and captain Steven Smith, who combined for 130 runs, within 13 runs.
Peter Handscomb, who had displayed admirable grit in the series against India, cut a short ball from Taijul but the edge flew to first slip where Soumya Sarkar produced a brilliant reflex catch on the second attempt to give Bangladesh hope.
"We let ourselves down a bit in the first innings with the bat", Smith said.
Australia face a monumental battle to avoid an embarrassing defeat to Bangladesh which would leave them at risk of falling to their lowest ever Test ranking.
Australian spinner Steve O'Keefe has been recalled in the national squad as a replacement for injured Josh Hazlewood for the second Test of the two-match series against Bangladesh, beginning September 4 in Chittagong.