Vince and Billings fought hard for England, but their total of 208 was not enough to win.
Australia beat England with a score of 280 for 8 (Smith 94, Labuschagne 58, Marsh 50, and Rashid 3-57).
Smith's 94 from 114 balls was the most important part of Australia's innings, along with Marnus Labuschagne's easy half-century and Mitchell Marsh's harder work.
But Vince swung across the line at Hazlewood, and the umpire called lbw.
The always-reliable Zampa then made the decisive breakthroughs in the middle order, including Billings for 71, as he took 3 for 0 in nine balls and England lost 7 for 52.
This time, there wasn't enough bats to go around.
Smith and Labuschagne added 101 runs in 19 overs for the third wicket. After Rashid took two wickets in two balls, Smith and Marsh added 90 runs for the fifth wicket.
Smith wasn't as smooth as he was two days ago in Adelaide, when he said it was the best he'd felt at the crease in six years.
However, he moved into the 90s with a flick for six over backward square leg off Sam Curran.