It was a first victory in 10 tests for Australia after losing a series 4-0 in India and another in England 3-0 this year, and a first win in eight Ashes contests since the Perth test in 2010. (Agencies)
Only the weather, which delayed play twice for a total of more than two hours, looked like extending the contest to a fifth day but Johnson put paid to that idea when he dismissed James Anderson caught and bowled in fading light at the Gabba.
England's hopes of a result at Brisbane had been slim at best when they were set 561 to win and lost two second innings wickets for only 24 runs on Saturday evening.
They were shattered when the dismissal of captain Alastair Cook for 65 triggered a collapse from 142 for four to 160 for eight in the 45 minutes between the two weather disruptions.
Left-arm quick Johnson, who took 4-61 as the tourists were skittled for 136 in their first innings, claimed his eighth test five-wicket haul to walk away with the man of the match award.
"A fantastic start, some fantastic individual performances, no more so than Mitchell Johnson," said Australia captain Michael Clarke.
It was spinner Nathan Lyon (2-46) who made the key breakthrough, though, by dismissing Cook.
Cook, who scored 235 not out in his second innings in the last Ashes test at the Gabba, had played a composed and defiant innings with just three boundaries before a dramatic hailstorm forced the players off the field.
Six balls after the resumption, Lyon got a little bit of extra bounce out of the surface and Cook caught a top edge with an attempted cut with Brad Haddin taking the catch behind the wickets.
England were only able to add only six runs for the next three wickets with Matt Prior (4), Stuart Broad (4) and Graeme Swann, whose miserable match continued when he got a second duck, quickly following their captain back to the pavilion.
As in the first innings when England lost six wickets for nine runs in one spell, Lyon was just as involved as Johnson and it was he who had Prior caught at leg slip by David Warner after just eight minutes in the middle.
A bullish Broad lasted just three deliveries and five minutes before he got the faintest of touches to a Johnson delivery which again Haddin snaffled up.
Swann lasted just two balls before a meek fend at a Johnson snorter saw the ball fly into the hands of a diving Steve Smith in the slips.
England regrouped sufficiently to survive until the rain starting falling again but the storm passed reasonably quickly and the players were back out with an hour of play remaining.
It was a first victory in 10 tests for Australia after losing a series 4-0 in India and another in England 3-0 this year, and a first win in eight Ashes contests since the Perth test in 2010.