England, already an irretrievable 3-0 down in the five-match series, dismissed Smith, Mitchell and Shaun Marsh, Tim Paine and Jackson Bird to take five for 82 in the first session in baking temperatures.
Debutant Tom Curran celebrated his first Test wicket as Smith chopped a short, wide delivery on to his stumps on 76, just 30 minutes into the second day's play.
It was the first of three similar drag-on wickets for England's bowlers on a slow-paced MCG pitch. At lunch, Pat Cummins was batting on four not out with Josh Hazlewood yet to score.
In the previous three showpiece Boxing Day Tests, Smith had scored 192 against India, 134 not out against the West Indies and an unbeaten 165 last year against Pakistan.
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Smith threw his head back in annoyance as the bails flew into the air. With his dismissal Smith has now scored 502 runs in the Ashes series at a stunning average of 125.50.
It was an overdue slice of luck for Curran, who had David Warner caught on 99 only to have the dismissal overturned for an overstepping no-ball on Tuesday's opening day. Warner went on to score 103.
His elder brother, Shaun, lost a leg before wicket review on 61 off 148 balls to Stuart Broad.
It was Shaun Marsh's second half-century of the series after scoring an unbeaten 126 in the second Adelaide Test.
Paine became the third batsman to chop on to his stumps in the session for 24, giving James Anderson his second wicket, while Bird fell leg before wicket to Broad for four.