Neser became the first player in a decade to score a century and take a five-wicket haul in a first class match, a feat emulated later in the day by WA's Ashton Agar against South Australia.
His dashing 121 lifted the Bulls to a total of 529, with great support from Jimmy Peirson (62) and the rest of the lower order.
Neser, who had previously scored a List A hundred for Queensland, brought up his maiden first-class century with consecutive boundaries thrashed through the leg side. It followed his opening-day figures of 5-32 to help bowl out Tasmania for 250.
It was the sixth time a Queenslander has scored a century and taken a five-wicket haul in a Shield match, with Ashley Noffke the last maroon to achieve the feat in 2007-08 against Tasmania at the Gabba. Neser joins Noffke, Phil Carlson, Ron Oxenham and Col McCool (twice) in that select group.
Carlson is the only player to score a century and take 10 wickets in a game for Queensland, with the Australian Test and ODI allrounder producing his mighty performance against NSW at the Gabba in 1978-79.
The Bulls then turned the screws on the Tigers, reducing them to 3-86 at stumps, still trailing by 193 entering the final day of the opening round.
Meanwhile Queensland will return home tomorrow after Cricket Australia re-scheduled parts of the next two rounds of the competition due to after effects of COVID-19 quarantine.
Victoria’s round two match against New South Wales will not take place as scheduled. New South Wales will take on Western Australia at Park 25, with Victoria and Queensland to have a bye.
The delayed round one match between New South Wales and Victoria, originally scheduled for November 17-20, has also been postponed until after the KFC Big Bash League season to allow players adequate time to prepare for that competition.
The Bulls players will be available for Sci-Fleet Motors Premier Cricket duties this weekend, including the second day of the Bulls Masters Premier Cricket round and the Kookaburra One Day competition Final between Redlands and Norths at Allan Border Field on Sunday.
October 19-22: South Australia v Tasmania, Karen Rolton Oval
October 19-22: Western Australia v New South Wales, Park 25
Byes: Queensland, Victoria