Adam Voges added 72 and Shane Watson 68 as the tourists posted an imposing 345.
It was sensational stuff from Smith, who began his haul when he yorked Australian Voges for one.
He was eventually stumped off Daniel Vettori but Cameron White and Adam Voges saw Australia home on 248-4.
But Voges was 54 not out at tea, and found further support from Pomersbach early in the final session.
Adam Voges hit a rapid 68 and Samit Patel 47 for the hosts, while Naqaash Tahir picked up 4-89.
Voges then became Willoughby's fourth victim, adjudged leg before wicket to an inswinger.
The hosts' total of 151 for seven was built around 51 from overseas batsman Adam Voges, who faced 42 balls.
But they were pegged back by Adam Voges who picked up Joyce for 42 with his first ball and finished with 3-25.
With the ball set to fly for six, long-on fielder Voges made the catch on the boundary, but his body's momentum took him over the rope.
Symonds, whose last Test was against South Africa in April, held off competition from uncapped batsman Adam Voges to make the starting line-up.
Adam Voges (72) and Wes Robinson (62) put on 87 in 22.5 overs as England proved less of a force in the afternoon heat.
But under sunnier skies than on day one, Voges and Brown came together to put on 119 for the fifth wicket either side of lunch.
Warner and Ferguson fell soon after before Hussey steadied the innings with a composed 41 off 39 deliveries, ably assisted by Voges (23), Cameron White and James Hopes (both 16).
However, the complexion of the match changed courtesy a moment of inspiration from Adam Voges when McCullum launched a Ben Hilfenhaus length ball down the ground in the 19th over.
Australian Voges played a more textbook innings, although he did survive on 18 when Craig Kieswetter failed to cling on to a difficult chance down the legside.
On a slow, turning pitch, the Nottinghamshire batsmen struggled to time the ball for much of their innings and were thankful to Voges for helping them to a half-decent total.
Sreesanth ended the partnership with a double strike just after lunch, Voges edging to Bell at gully and Ali Brown fending a rising ball to Rikki Clarke in the slips.
His 114-run stand with Voges (74), from 83 balls, paved the way for Australia's total, their biggest on British soil, after Watson's breezy 68 at the top of the order set the tone.
But, with the scoreboard at 43-3, in-form Aussie Adam Voges counter-attacked in attractive fashion, pulling two consecutive deliveries from Boyd Rankin for six as he and Patel put on 98 in 17 overs.
Southee then removed Cameron White (six) and Adam Voges (five) while Nathan McCullum picked up his first one-day wicket when he had opener Shane Watson (53) caught by Taylor to leave the tourists 96-5.
In the next over, Voges contributed to his own downfall only four runs later, taking off for an unwise single to cover and beaten to the non-striker's end by a direct hit from Collingwood.
However, the 12-man squad includes Adam Voges, Luke Pomersbach and Luke Ronchi, who have all played one-day internationals or Twenty20 internationals for the full Australia side, while Steve Magoffin has experience of English county cricket.
Sidebottom also removed Jim Troughton and Tim Ambrose lbw in an opening spell of three for 11 from nine overs, while Shreck's out-swinger was too good for Trott, who edged low to Adam Voges at second slip.
We've used a lot of different players, we've seen very little of Stuart Broad and Graeme Swann, a little bit of Ryan Sidebottom and having three different overseas players (Hashim Amla, David Hussey and Adam Voges) is not easy.
Chris Cairns and Chris Read quickly followed as the run-rate slowed in the middle overs, with Voges pulling Du Plessis to the waiting Flintoff at deep mid-wicket, leaving Mark Ealham to hit two sixes in a late cameo of 28 off 21 balls.
Southee picked himself up to dismiss Mike Hussey for nine but the game was firmly in Australia's grasp when Haddin was lured out of his crease by Vettori and White helped himself to an unbeaten 25 before Voges hit the winning boundary to finish on 13 not out.
When White fell for 51 and Adam Voges and James Hopes both fell cheaply it looked as though Australia were in danger of losing their way, but Hussey accelerated superbly at the death, hitting Praveen for 18 runs in an over and helping Australia to a decent total.
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