With the win, the hosts made it 1-2 and kept their hopes alive of winning the five-match series. The Three Lions won after rain halted play with their score at 254 for four while chasing 305. Australia's 14-match winning streak in ODIs also ended.
After being asked to bat first, the Aussies put up a healthy score of 304 for seven on the board.
Matthew Short (14) and Mitchell Marsh (24) failed to convert their starts. But it was a partnership of 84 runs between Steve Smith and Cameron Green that steadied the ship. Batting at No.3, Smith scored 60 runs off 82 balls with five fours before Jofra Archer accounted for his wicket.
Green also contributed with 42 runs. Labuschagne fell for a duck, but Alex Carey, Australia's hero from the second ODI, played his shots to stay not out on 77 off 65. Glenn Maxwell and Aaron Hardie's knocks of 30 and 44 respectively helped Australia go past the 300-run mark.
Archer picked up two wickets while Brydon Carse, Jacob Bethell, Will Jacks and Liam Livingstone got one scalp apiece.