James Anderson took his first wicket of the Ashes opener but he could not stop Australia from closing in on England's first-innings total at Edgbaston on Sunday.

England great Anderson bowled Alex Carey on the third morning only for Australia to be 365-6 after an hour's play.

That left the Ashes-holders just 23 runs adrift of England's 393-8, a total built on Joe Root's unbeaten 118 and featuring Jonny Bairstow's run-a-ball 78.

Usman Khawaja had extended his overnight 126 not out to an unbeaten 139, with Australia captain Pat Cummins 23 not out. 

Australia resumed on 311-5, 82 runs behind, with Khawaja having ended his decade-long wait for an Ashes hundred in England after overseeing a recovery from 67-3. 

Carey was then 52 not out.

Both batsmen should have been dismissed Saturday, with Khawaja bowled off a Stuart Broad no-ball on 112 and Carey dropped by opposing wicketkeeper Bairstow on 26.

Bairstow gave Carey another reprieve off just the fourth ball of Sunday's play.

Carey had failed to add to his overnight score when he inside edged a drive off Anderson only for Bairstow to drop the one-handed chance as he dived to his right.

It was the third chance Bairstow, preferred behind the stumps to Ben Foakes -- arguably a better keeper but not as good as a batsman -- had missed. He had also fumbled an opportunity to stump Cameron Green.

But Anderson, the most successful fast bowler in Test history but wicketless on Saturday, then took matters into his own hands, the 40-year-old bowling Carey between bat and pad with a ball that jagged back sharply.

Carey was out for 66, having helped Khawaja add a valuable 118 to take Australia to 338-6.

New batsman Cummins got Australia even closer to level terms by launching off-spinner Moeen Ali for two sixes.

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