Fast bowler Archer, in only his second Test, took 6-45 in 17.1 overs -- the first time he had taken five or more wickets in an innings at this level after marking his debut with a 92 mph bouncer that concussed Smith and ruled him out of this match in the rain-affected drawn second match of the series at Lord's.
Australia were dismissed inside 53 overs after losing their last eight wickets for a mere 43 runs on a day featuring several weather interruptions.
England, looking to level the five-Test Specsavers series at 1-1, reduced Australia to 25-2 after home captain Joe Root won the toss.
But David Warner (61) and Marnus Labuschagne (74) revived the innings with a third-wicket stand of 111.
Archer, however, turned the tide by having Warner caught behind off a 90 mph delivery.
It was the start of a collapse that saw Australia lose three wickets for three runs to be 139-5.
Travis Head was bowled for a duck by Stuart Broad and Matthew Wade, a century-maker in the first Test, also fell for nought when an Archer delivery deflected off the thigh pad via his glove and into the base of the stump.
"It was stop-start all day, which is really annoying," 24-year-old Archer told the BBC.
"I'm over the moon to get six wickets but equally happy just to get off.
"The ball just started swinging randomly from the over before the Warner wicket."
Warner's innings was his first double figure score of a series where he had previously managed just 18 runs in total, while Labuschagne struck his second successive fifty after making 59 as a concussion substitute for Smith at Lord's.
"I was always confident I could find form," said the experienced Warner, like Smith playing in his first Test series since they each completed a 12-month ball-tampering bans.
"Good balls were getting me out and that happens. You just have to work out how to survive."
Meanwhile, Warner compared Barbados-born Archer to South Africa fast-bowling great Dale Steyn.
"I look at him like Dale Steyn, searching for swing and movement early on but then ramping up their speed later," said Warner.
"That is world-class bowling and England have a great prospect."
Root was hoping to make the most of overcast conditions at his Yorkshire home ground -- and Smith's absence.
Smith's scores of 144, 142 and 92 had been central to putting Ashes-holders Australia ahead as they look to win a Test series away to England for the first time in 18 years.
Warner had previously managed innings of just two, eight, three and five this Ashes.
Butit was fellow top-order left-handers Marcus Harris, recalled in place of the dropped Cameron Bancroft, and Usman Khawaja who both fell cheaply, for eight apiece, on Thursday.
Archer, bowling from around the wicket, squared Harris up with an 87.3 mph ball and had him caught behind by wicketkeeper Jonny Bairstow.
Moments later, with Australia 12-1 off four overs, rain stopped play.
When play resumed, Khawaja's glance off Broad was caught by Bairstow.
More rain and bad light -- even though the floodlights were on -- halted play in the second session.
The resumption saw an increasingly assured Labuschagne hit two well-struck fours off first-change Chris Woakes.
Warner's mistimed four off Ben Stokes saw Warner complete a 79-ball fifty -- a landmark greeted with now familiar boos.
But there were cheers too, with Warner's wife Candice among those at the ground applauding her husband's innings.
Labuschagne's gutsy 129-ball innings ended when he was lbw to Stokes after missing a full toss, with Archer finishing the day's play when he had Nathan Lyon leg before.