At the close of play, England were 9/0 in their second innings with Rory Burns (4*) Joe Denly (1*) who will resume the play on day 3.
Archer returned with magical figures of 6/62 after rattling the Australian batting order. He was ably supported by Sam Curran (3/46), whose haul included a two-wicket burst in two deliveries.
But none of them could get Smith out as he brought up his 10th consecutive Ashes fifty. He hit Jack Leach for a four to bring up his half-century off 91 balls, thus becoming the player with the most successive 50-plus scores against a single opponent.
Smith surpassed former Pakistan skipper Inzamam-Ul-Haq who hit nine half-centuries in a row, also against England.
Just when Smith was looking set for a hundred, Chris Woakes (1/51) came back for a second spell and trapped him in front with a straight delivery. Smith faced 145 balls for his 80, hitting nine fours and a six.
Besides Smith, Marnus Labuschagne missed out on a half-century as he was dismissed for 48 just after lunch. Smith and Labuschagne shared a 69-run stand for the third wicket before Archer trapped the latter plumb in front.
Curran, playing his first Test in the series, got rid of Time Paine (1) and Pat Cummins (0) off successive deliveries but failed to bag a hat-trick. Archer then removed the tail although Nathan Lyon fought well for his 25 to trim the deficit down to below hundred.
Earlier, David Warner failed once again, as Archer had the out of sorts southpaw caught behind by Jonny Bairstow for just five. Harris too was dismissed for three after he edged Archer to Ben Stokes at second slip, leaving Australia reeling at 14/2.