The hosts' victory ensured the two-match series finished level 1-1.
Smith's top-score was spiced with six fours and four sixes and piloted the West Indies to 160 all out off 19.4 overs.
Australia's chase was boosted by David Warner's 58 off 43 deliveries but once he was run out, the momentum shifted and they fell short at 146-9 off 20 overs.
Paceman Edwards claimed 3-23, including two in an excellent penultimate over, while Samuels took crucial middle order wickets on the way to 3-23.
Dwayne Bravo's direct hit run out of Warner was vital, and he also grabbed 2-27.
Edwards set back Australia's pursuit early as he claimed Watson to a slip catch by West Indies skipper Darren Sammy. But Warner and George Bailey soon shifted the balance in a stand of 63 in 6.3 overs.
Bailey, dropped early on off Edwards, struck two fours and a six in 24.
Samuels broke the partnership when Bailey top-edged a slog-sweep into the leg-side. The flat off-spinner also removed the dangerous Michael Hussey (14) at 89-3 in the 12th over.
The West Indies grabbed the vital wicket of Warner through the brilliance of Bravo, who pinged the stumps from deep midwicket as the batsmen sought two runs.
Left-hander Warner slammed five fours and three sixes.
David Hussey and Matthew Wade renewed Australia's hopes with a stand of 35 for the fifth wicket. But, with 28 needed from three overs, Samuels claimed Wade and conceded just three runs in the 17th over.
Edwards removed Daniel Christian (3) and Brett Lee (0) off consecutive balls and Australia were left with too much to do.
With 19 needed off the last over, Dwayne Bravo ensured there were to be no late drama, Pollard hauling in a fantastic catch in the deep to end David Hussey's resistance and spark wild celebrations in the crowd.
Earlier, Smith and Johnson Charles (37) provided the hosts with a frenetic start but a clatter of late wickets helped Australia keep the target manageable.
The West Indies stumbled badly from 110-3 off 10 overs, only realizing 50 runs off the final 10.
Smith and Charles excited a huge crowd of 11,500 with a boundary-studded opening stand after the West Indies won the toss. Charles lashed six fours and a six before he departed, holing out off Watson at 72-1 in the seventh over.
Smith continued to play some majestic strokes, racing to his half century off 30 balls with three huge sixes in one James Pattinson over.
The first landed in the Greenidge & Haynes Stand at midwicket, the second went straight and further, into the top deck of the Hall & Griffith Stand, the third even straighter into the spectators in the Three Ws Stand.
But Lee claimed Pollard cheaply and when Smith fell to left-arm spinner Xavier Doherty trying to hit another six, Australia's fightback was on.
Only Bravo, with 23 off 24 deliveries, managed any significant contribution in the late order.