Australia appealed, more in hope than confidence, and the television umpire studied a long series of slow motion replays before deciding that Bopara's foot had come up just as the bail had been removed. He was out and with him went England's last chance of victory.
His departure left England's last pair at the crease, needing nine runs with eight balls remaining. Chris Jordan and James Tredwell reached the last over with eight runs still required and reduced the target with a single and a leg bye before Tredwell was caught by Wade off Shane Watson to end the innings.
McKay finished with 3-36, including the wickets of Bopara, Ben Stokes (0) and Stuart Broad (7).
Nathan Coulter-Nile took 3-34 and James Faulkner 2-37 in an outstanding Australian bowling performance.
"After we got the last wicket, that's when I thought we had it won," Australia captain Michael Clarke said. "A magnificent performance by the boys with the ball today.
"I thought our batting was disappointing but I guess we had to have that belief we could still win the game. The execution through the powerplay and at the end ... the boys did an outstanding job.
"For me it was about trying to find a way to take 10 wickets and the bowlers executed well. They deserve a lot of credit."
Scoring runs on a holding Adelaide Oval surface required patience and perseverance that only a handful of batsman showed. George Bailey top-scored with 56 and
Shaun Marsh made 36 in the Australian innings while Alastair Cook gave England a sound start with a careful 39.
England's run chase still seemed relatively undemanding but the only point at which they seemed in command was when Root and Morgan were together.
