Smith, tied down by England's modern-day 'Bodyline' fielding strategy, kept Australia's hopes flickering with his resilient knock in an absorbing struggle between bat and ball.
The tourists view Smith -- the world's top-rated batsman -- as their number one target as the home side chipped away at England's 302 first innings.
At lunch, Australia were 213 for seven, trailing by 89 runs with Smith holding firm on 81 and Pat Cummins on two. Smith added just 17 runs in the two-hour session.
Root showed his tactical acumen with inventive field settings, particularly when Smith was on strike.
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The England skipper placed six fielders on the leg-side with three in the deep and had no-one in front of the bat on the off-side while his pacemen bowled short-pitched deliveries to Smith.
While Smith was at the crease, Australia still had hopes of closing in on England's first innings total in a low- scoring contest as the home side battled for runs under concerted pressure.
Marsh reached his first Ashes fifty and eighth in Tests before he was deceived by a slower ball from Stuart Broad and lobbed a catch to James Anderson at mid-off.
Marsh, recalled for an eighth time to the Test team, made 51 off 141 balls and put on 99 runs with Smith for the fifth wicket.
Paine, back for his first Test in seven years, stayed at the crease for an hour before he was dislodged by a smart one-handed catch by wicketkeeper Jonny Bairstow off Anderson for 13.
Smith had a moment on 69 when a rearing Jake Ball delivery hit the top of his bat but fell out of the reach of a close-in fielder.