Helped by the catching magic of home captain Steve Smith, 35-year-old Neser finished with 5-42 at his home ground in his first Test in three years, leaving the hosts needing 65 runs to win the day-night match.
While England quick Gus Atkinson grabbed two wickets, opener Jake Weatherald (17 not out) and number four batter Smith (23 not out) mowed down the target after dinner, condemning England to a 15th loss in their last 17 Tests in Australia.
England seamer Jofra Archer had a heated exchange with Smith in the final overs but ended up getting smashed for two fours and a six by the fired-up skipper.
Australia finished on 69 for two and Smith sealed the win in style, thumping Atkinson for another six over deep square to the delight of the home fans in the crowd of 27,888.
"What I said to Archer stays on the field. It was good banter," said Smith, who charged to his 23 in nine balls.
"I thought the boys played exceptionally well.
"The adrenaline was pumping at the end there ... It was a huge win, obviously great to go 2-0 up."
With Adelaide to come among three matches left in the series, England captain Ben Stokes refused to concede the urn was lost after battling hard in a 152-ball 50.
"I absolutely believe in that dressing room," he said.
"We know we have to win these next three games.
"We won't shy away from the battle but we need to sort things out pretty quick if we want to bring the Ashes back to England."
It would nonetheless take something extraordinary for England to win it from here.
Only one team has ever come back from 2-0 down to win a series in nearly 150 years of Test cricket - Don Bradman's Australia in the home Ashes of 1936/37.
In Brisbane, Stokes's England showed their fans little to suggest a Bradman-esque effort is within them.
