Batting at No 8, Ali, who made his name as a top-order shotmaker, struck a rapid 77 to help boost England's first innings total to 430 all out -- the first time they had passed 400 in three Ashes series.
The off-spinning all-rounder then captured the prize wickets of Steven Smith, the world's number one ranked Test batsman, and Australia captain Michael Clarke, who both fell to him in the 30s.
"I think we're ahead," said Ali, who shot to prominence last year with 14 wickets in England's home series win over India.
"That last wicket put us into pole position a bit more."
Both Ali and Australia off-spinner Nathan Lyon have been targeted by opposition batsmen already this match as both sides look to take an aggressive approach.
However, Ali was able to outwit Smith on Wednesday when he spotted the batsman's charge and induced a leading edge which was caught by England captain Alastair Cook at a short mid-on position.
"He can take you down, but he can also give you a chance -- and I'm always telling myself that I'm one ball away from getting a wicket," added the 28-year-old Worcestershire all-rounder, who also caught and bowled Clarke.
"I think these guys (Australia) are going to try to attack me a little bit more than India did last year.
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