The 25-year-old anchored the Australian innings during his 118-ball 101 and hit six boundaries and two sixes after Australia decided to bat on a flat Sharjah Stadium pitch.
Smith walked in as early as the second ball of the match when opener Aaron Finch was caught off a casual shot at point from lanky paceman Mohammad Irfan.
Smith consolidated the innings with an 86-run second wicket stand with David Warner (43) and another 37 with skipper George Bailey (18) for the third wicket.
Dashing all-rounder Glenn Maxwell (21) failed to take advantage of two dropped catches as he gave away his wicket to debutant spinner Zulfiqar Babar.
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Afridi was the best Pakistani bowler with 3-46, after going wicket-less in his last six matches.
Smith too holed out off Afridi in the 45th over, leaving Brad Haddin (23 not out) and Mitchell Johnson (21) to give the final touches.
Smith's previous best of 46 not out came against England at Adelaide in 2011.
Pakistan gave a one-day debut to Babar to shoulder the spin attack in the absence of Saeed Ajmal, who was suspended for an illegal bowling action last month and is not on the tour.
Australia handed a one-day debut to Sean Abbott after the 22-year-old paceman impressed in his team's six-wicket win in the only Twenty20 match in Dubai on Sunday.
The remaining one-day matches will be played in Dubai (October 10) and Abu Dhabi (October 12). The one-days will be followed by two Tests.