Australia dismissed England, chasing a target of 561, for 179 in their second innings in the last session of the fourth day of the match as left-arm pacer Mitchell Johnson picked up five wickets for 42 runs.
Johnson was named Man of the Match for his scores of 64, 39 not out and a nine-wicket match haul.
Meanwhile, Cricket Australia (CA) Sunday retained the same squad which won the first Ashes Test by 381 runs against England in Brisbane.
However, another player might join the squad ahead of the next match.
"An additional player may be included after the National Selection Panel has inspected the Adelaide Oval pitch," a CA statement said.
The second Test will be held from December 5 to 9.
Australia's second Test squad: Michael Clarke (captain), Brad Haddin, George Bailey, James Faulkner, Ryan Harris, Mitchell Johnson, Nathan Lyon, Chris Rogers, Peter Siddle, Steven Smith, David Warner, Shane Watson.