Steve Smith struck a fine 93 to help Australia reassert control of the second Ashes Test on Friday after England grabbed early wickets on day two, including Marnus Labuschagne for 103.

The home side stretched their lead to a commanding 390 for seven at tea in the day-night clash in Adelaide, with Mitchell Starc unbeaten on three.

Alex Carey fell for 51 -- his maiden Test half-century -- on the stroke of the break, chipping to Haseeb Hameed at cover off Jimmy Anderson.

Stand-in captain Smith was England's key tormentor at the last Ashes in 2019, on his return from a ball-tampering ban, and he kept his cool in sweltering Adelaide.

He was ably supported by Carey, who is in the team as replacement wicketkeeper for former skipper Tim Paine, who quit on the eve of the Ashes over a text-message scandal.

Smith came to the crease when David Warner was out for 95 and barely put a foot wrong, dishing out particular punishment to Chris Woakes, crunching three boundaries in one over then smacking him for a big six.

He looked destined for a 28th Test century but was dismissed lbw to an Anderson ball that pitched up -- the English veteran's first wicket of the tour.

Unflappable number three Labuschagne earlier completed his epic century after setting himself up by batting almost all day on Thursday, coming to the crease when Marcus Harris fell cheaply to Stuart Broad.

He brought up his sixth Test ton and first in an Ashes series off a dogged 287 balls with a boundary off Anderson.

But Labuschagne struggled when Ollie Robinson was brought into the attack and was trudging to the pavilion when he was caught by England wicketkeeper Jos Buttler on 102.

However, replays showed it was a no-ball and the batsman headed back to the crease, only for the grin to be quickly wiped off his face minutes later when he was trapped lbw by Robinson, adding just eight runs to his overnight 95.

"It was nice to get that hundred, obviously got a few chances there but that's how it goes sometimes, you ride your luck," Labuschagne said.

"It feels like you have to grind for every run that you're out there."

Temperatures in Adelaide peaked at 37 degrees Celsius (99 Fahrenheit) with England toiling in stifling heat, desperately needing wickets to stay in the game.

They were rewarded for their persistence by getting not only Labuschagne but Travis Head, who was high on confidence after an impressive 152 in the first Test at Brisbane.

But he was undone by Joe Root's part-time spin, with the England captain finding turn and bounce with the pink ball, beating Head with a delivery that left him sprawled on one knee in disbelief, gone for 18.

Root has sent down 20 overs with no other slow ball options after England left out off-spinner Jack Leach in favour of five quicks. 

The lanky Cameron Green only lasted five balls, out for two with a fuller delivery from Ben Stokes clattering into his off-stump -- the star all-rounder's second wicket after snaring Warner.

The hosts lead the five-match series 1-0.