Jos Buttler added just six runs to his overnight score of 64, bowled by Pat Cummins off the pad attempting a big heave down the ground, before Jack Leach's resistance subsided in the next over.
Mitchell Marsh´s dismissal of Leach gave him figures of 5-46 on his return to the Test side while Cummins took 3-84.
Buttler, whose previous eight innings in this series had produced a best of 41, deposited Josh Hazlewood for three sixes on Wednesday.
Smith (59no) headed into the game with 671 runs in the series and extended that to 730 by tea in south London after notching his sixth fifty-plus score in as many innings this summer and 10th in a row against England.
"It probably wasn't reflected in our first session but you drop catches sometimes". Root enjoyed a milestone moment on Thursday when he became the 12th England batsman to register 7,000 Test runs.
But he showed just why selectors have kept the faith, taking four wickets to leave the field as Australia's best bowler in his first Test since being parachuted in on Boxing Day against India last summer. Both drops were off Cummins.
The batsman pushed unnecessarily at a wide one and Steve Smith held on to complete a juggling catch at second slip.
Jonny Bairstow followed shortly afterwards, lbw to Marsh for 22.
There was no doubt over the contact when Archer dismissed Harris, a thick edge well picked up by Ben Stokes at second slip, bringing Smith to the middle.
Rory Burns once again made a decent start, and once again Joe Root chipped in, but neither made the Smithian contribution demanded of them, leaving the scoreboard on the dreary side once the all-too common collapse occurred.
Australia won at Old Trafford last week to take a 2-1 lead in the five-match series, meaning they will retain the urn regardless of the result at the Oval.