Former Australia captain Ricky Ponting Saturday called for cricket to ditch its requirement to have neutral umpires after a number of incorrect decisions in the first Test of the Ashes series in England.
Smith's arrival at the crease prompted a huge chorus of boos from England fans who earlier in the day had taunted him with chants of "Crying on the telly, we saw you crying on the telly" in a reference to the star batsman's emotional press conference in Sydney after he was sent home from South Africa.
The Australian team competes against England in the Ashes Test at Edgbaston.
Australia tried their hand at the short ball only towards the end of the first hour, and reaped rewards soon after the drinks break when Broad, on 29, miscued one to fine leg. Woakes played a mature hand right through the session, topping off his bowling skills recently on display at Lord's with his batting skills here at Edgbaston.
Former captain Smith has already marked his first Test match since completing a 12-month ban imposed by Cricket Australia for his role in a ball-tampering scandal in South Africa past year with a brilliant century.
The tourists crashed to 2-27 in Birmingham before Smith, who will resume on 46, steadied with help from Usman Khawaja (40) and Travis Head (21 not out). The upshot was that, by the close of play, Australia's run rate was exactly four runs an over.
Ashes debutant Burns was caught behind off the bowling of off-spinner Lyon for 133, his maiden Test century, after a superb feat of endurance that saw the opener spend almost eight hours at the crease.
England lost three wickets for four runs before lunch to slump to 300-8 - just 16 runs ahead.
However, England lost three wickets in 11 balls before Stuart Broad and Chris Woakes came to the rescue by adding 65 runs for the ninth wicket.
Australia fast bowler Pat Cummins took 3-84 in 33 overs on a placid but wearing pitch and off-spinner Nathan Lyon 3-112 in 43.5 overs. Ben Stokes was unbeaten on 38.
England started well as Stokes passed 50 in front of a raucous crowd but nicked the ball through to Tim Paine the very next ball.
Burns battled through what felt like an eternity in the nervous 90s, during which Joe Denly and Jos Buttler both departed amid an Australian fightback, and faced some 10 balls on 99.
It all happened on the last delivery of the 105th over when Ali's shouldered arms to a straight delivery from Lyon.