England, set what would have been a new fourth-innings record of 509 for victory, collapsed to 103 all out after tea on the fourth day.
Left-arm fast bowler Johnson took three for 27 as England were dismissed in a mere 37 overs.
It was only the ninth time in the 138-year history of Test cricket a side had won by more than 400 runs.
Australia's fast bowlers are appreciably quicker than their England counterparts and sheer pace was responsible for several wickets as the home side suffered the latest in a long line of top-order slumps.
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The more realistic if still difficult task for England, 1-0 ahead in the five-match series after their 169-run win in the first Test in Cardiff, was to bat out the remaining 155 overs left in the match to secure a draw.
Only eight sides, however, have survived for more than the equivalent of 150 six-ball overs to draw a Test match.
Opener Adam Lyth, out for a duck in the first innings, could only manage seven on Sunday before pushing at a lifting ball from Mitchell Starc he was caught behind by debutant wicket-keeper Peter Nevill.
England captain Alastair Cook, who batted for nearly six hours in making 96 during the first innings, certainly had the temperament required for the tricky situation.
But his technique deserted him when he tried to cut Johnson's fourth ball of the innings without moving his feet and was caught behind for 11.