Pakistan responded well until off-spinner Nathan Lyon claimed two wickets in two deliveries, including that of rival skipper Misbah-Ul-Haq, in the 13th over to turn the match on its head as Australia took 1-0 lead in the three-match series.
Opener Sarfraz Ahmed (34) and Umar Akmal (46) provided some resistance with the bat before Pakistan folded for 162 in the 37th over.
"Very pleased (with the performance)," Bailey said at the presentation ceremony. "I thought we were maybe 15-20 runs short with the bat but outstanding performance with the ball...a pretty good all-round performance."
Lyon and fellow off-spinner Glenn Maxwell claimed two wickets apiece while Mitchell Johnson (3-24) proved a quality pace bowler can succeed even on a docile, spin-friendly surface.
Earlier Smith's brilliant century notwithstanding, Australia did not get the late burst that could have taken them past the 275-mark.
Shahid Afridi (3-46) was the pick of the Pakistani bowlers who conceded 37 runs in the first 10 overs and 64 in the final 10 to restrict Australia to a modest total at the Sharjah Cricket Ground.
Towering left-arm paceman Mohammad Irfan gave Pakistan a dream start when he dismissed Aaron Finch with the first delivery of the match with Ahmed Shehzad taking a brilliant catch at point.
Smith walked in to partner David Warner for a steady 85-run partnership before Afridi separated them in his second over.
Warner pulled the leg-spinner to mid-wicket to depart after a 63-ball 43 that included five boundaries.
Bailey hit Fawad Alam for a six but perished the very next ball trying to repeat the shot only for Afridi to take a tumbling catch after running backwards from midwicket.
Maxwell, man of the match in Australia's victory in the lone Twenty20 match on Sunday, could not capitalise on the two reprieves he got off Afridi and fell to debutant Zulfiqar Babar for 21.
Afridi dealt the biggest blow when he removed Smith in the 45th over, ending the 25-year-old's 101 off 118 balls that included two sixes and six fours.
The departure of Smith, by far their best player against spin, meant Australia could not launch a late assault and it took Johnson's 21-run cameo down the order to take them past the 250-mark.
"I enjoyed (batting at number three)," said Smith after collecting his man of the match award. "Looking for more opportunities and a few more big scores as well."
Dubai hosts the second match on Friday while the third and final match takes place in Abu Dhabi on Sunday.
(Reporting by Amlan Chakraborty; Editing by Toby Davis)
