Ali scored a quickfire 77 in England's first innings 430 -- the first time in three Ashes series they had passed 400.
The off-spinner then captured the key wickets of Steven Smith, the world's number one ranked Test batsman, and Australia captain Michael Clarke -- both out in the 30s.
Ashes-holders Australia, looking for a first series win in Britain in 14 years, were 264 for five at stumps.
That left them 166 runs behind and with much depending on their lower order if they were to prevent England establishing a significant first-innings lead.
After stumps, Ali told Sky Sports: "We were happy yesterday (Wednesday) and then today (Thursday) with the start we had and then taking five wickets.
"A couple of wickets tomorrow (Friday) with the new ball and we're right in it."
Reflecting on his innings, the 28-year-old Worcestershire all-rounder revealed he had taken his cue from England captain Alastair Cook.
"Cooky said for everyone to play the way they play, I felt I wanted to play my shots and entertain everyone," Ali explained.
There was heartache for Australia opener Chris Rogers who set a new record for most successive Test fifties without a hundred when his seventh straight half-century ended on 95.
He added: "I'm old -- I can feel it. Days in the field are hard work. Sometimes you think it's a young man's game."
England dismissed Australia dangerman David Warner for 17 when the opener edged James Anderson and Cook held a sharp catch at first slip.
Smith drove Ali for three fours in four balls but the bowler had his revenge.
An ungainly Smith, trying to avoid being stumped after Ali spotted his charge, got a leading edge and Cook, belying his reputation for cautious captaincy, held a catch having stationed himself in an unusual short mid-on position.
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