In a match in which the momentum see-sawed both ways on a number of occasions, Australia finally managed to consolidate their position on Day 4 thanks to centuries by Steve Smith and Matthew Wade.
England started Day 5 chasing a daunting target of 398 with 10 wickets in hand, but Pat Cummins made the early incision by dismissing first innings centurion Rory Burns in the 10th over of the innings.
Nathan Lyon then tore into the England top order, picking up the wickets of Jason Roy, captain Joe Root and Joe Denly to reduce the hosts to 85/4 at Lunch.
Australia never took the foot off the peddle, with Cummins dismissing Jos Buttler shortly after the restart. He then dismissed Jonny Bairstow before Lyon accounted for Ben Stokes in the next over.
Moeen Ali and Chris Woakes then held on to stitch together a stand of 39 runs with Woakes doing the bulk of the scoring. It was England's second highest stand of the innings after Roy and Root's 41-run second wicket partnership earlier in the day.
The partnership was broken when Lyon managed to get an edge off Ali which flew straight into the hands of David Warner at gully. Lyon's sixth wicket came off the very next ball when Stuart Broad edged him to Smith at slip.
The fall of the wicket saw the injured James Anderson come out to give Woakes company. While the pair held on for some time, the inevitable was completed when Cummins dismissed Woakes to hand Australia a 1-0 lead as they look to defend their Ashes crown.
Interestingly, the last time Australia started an Ashes in England with a win at Edgbaston was when they were being led by current team mentor Steve Waugh in 2001. That was also the last time they won the Ashes away from home.
Brief scores: 1st innings: Australia: 284 all out (Steve Smith 144, Broad 5/86); England: 374 all out (Rory Burns 133, Nathan Lyon 3/112); 2nd innings: Australia: 487/7 declared (Steve Smith 144, Matthew Wade 110, Ben Stokes 3/85); England: 146 all out (Chris Woakes 37, Nathan Lyon 6/49, Pat Cummins 4/32).
( With inputs from IANS )