Chasing 123 for victory, Australia crashed out in 13.4 overs with Shakib returning figures of 4-9 with his left-arm spin in the 60-run rout in the fifth match in Dhaka.
Australia’s previous lowest was 79 all out against England in 2005.
Pace bowler Mohammed Saifuddin combined with Shakib to rattle Australia with twin strikes in one over to send back Alex Carey and Moises Henriques.
Shakib wiped off the tail with the wickets of Nathan Ellis and Adam Zampa with nine of the 11 batsmen getting scores in single digits.
Earlier Mohammad Naim made 23 in Bangladesh’s 122 for eight after electing to bat.
Dan Christian and Nathan Ellis took two wickets each.
Bangladesh had secured their first series win over Australia after winning the opening three matches.