Smith agonised over whether to review Lyon's lbw shout that was turned down by New Zealand umpire Chris Gaffaney, having opted against referring an equally confident lbw appeal from Josh Hazlewood that came when Cook was on one.
On both occasions, ball-tracking technology suggested Gaffaney got it wrong.
Stoneman departed later in the session for 36, prodding at a wide delivery from Mitchell Starc to hand Usman Khawaja a low catch at gully.
Lyon, who has claimed more test wickets this year than any other bowler, continued his productive summer and regularly beat the bat.
Root, who was seven not out, was yet to bat at night in the game.
Anderson finished with figures of 5-43 from 22 overs, dismissing nightwatchman Lyon, Peter Handscomb and Starc as he continued a pink-ball masterclass that started under lights on day three.
● More people have attended the second Ashes battle between Australia and England than any other test match at the Adelaide Oval.
The Adelaide crowds for the test have, within four days, surpassed the oval's previous test-best aggregate of 172,361 in the infamous Bodyline test of 1933.
More than 22,000 spectators are in the oval yesterday, taking the aggregate to more than 172,600. The opening day of the test attracted 55,317 spectators, a record for test cricket at the venue near the city centre.
That number eclipsed the previous high of 50,962 who watched day one of the 1933 Bodyline test.
