Root, who eked out a half century under the Adelaide Oval lights, will probably need to stay out in the sun for much of the fifth day if he is to lead England to a first test win in Australia in almost seven years.
The result means that Australia has a ideal record in day-night Tests, having prevailed in all three of the pink-ball matches they have played in Adelaide, as well as the Test they won against Pakistan in Brisbane last summer.
A nerve-wracking 36 hours for Australia was erased in an instant by the big-right armer, and England are now facing a chastening series defeat at 2-0 down heading into the third Test in Perth.
The tourists resumed at 4-176 but paceman Josh Hazlewood struck with the second ball of the day, dismissing Chris Woakes (five) caught behind.
"I think we're still reasonably confident, obviously the last two days haven't gone to plan but I think we're still in front of the game", said Australia bowling coach David Saker.
The third test starts December 14 in Perth, where England is in danger of surrendering the urn after winning the Ashes on home soil in 2015.
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England's innings was rocking following the loss of James Vince to a horrid drive when Pat Cummins ripped a delivery through Joe Root, the ball flying to Tim Paine as the lights started to take effect.
The dismissal of Woakes had an element of fortune in that the feather the nightwatchman got on the ball was picked up by snicko but not the hotspot when it was referred.
Hazlewood then further dented England when he removed Joe Root (67) in his next over.
Moeen Ali and Jonny Bairstow had the potential to be a thorn in Australia's side, but such is Lyon's dominance over his rival spinner, it took only a few overs of probing off-breaks before Ali played an erroneous sweep and was trapped LBW. Starc ended with figures of 5/88.
"Disappointing", said Root. "I don't think we did ourselves justice". But we're still in the series. We showed that from the way we played yesterday.
Only one captain in the long history of test cricket had previously lost a test after opting not to enforce the follow-on and Smith was grateful to his bowlers for getting him out of a hole.