Smith, who scored his maiden Test ton in the last match of the Ashes series, was overlooked for Australia's current one-day tour of India.
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It hasn't impacted his form, with the 24-year-old scoring 70 and 47 in the condensed one-day tournament prior to his starring role on Sunday.
Earlier, Marcus North (51) was the best of the Warriors' batsmen - all of whom failed to cash in after making a start.
Smith came to the middle with NSW 1-46 after the dismissal of controversial opener David Warner for 17.
Abbott ensured the required run rate didn't get out of hand, thumping three sixes and a four as Smith brought up the winning runs in the penultimate over.
Abbott, who also claimed 2-43, was named man of the match.