The lanky left-armer's best one-day figures helped Australia keep their rivals down to 198 in 45.1 overs before they fought hard against Pakistani spinners to take a 1-0 lead in the three-match series at Sharjah Stadium.
Australia owed their run chase to some responsible batting by skipper Clarke (66), who added an invaluable 54 with Bailey for the fifth wicket before Baily-Glenn Maxwell (38) put on 63 for the sixth to see off the target in 48.2 overs.
Pakistan had attacked through their much-vaunted spinning trio of Saeed Ajmal (3-30), Mohammad Hafeez (2-29) and Shahid Afridi (1-37) but Australian batting was led by Clarke and finished by Bailey with an unbeaten 88-ball 57.
Clarke hit five boundaries during his 95-ball knock.
Ajmal struck with his first ball of the match, trapping a nervous Michael Hussey (five) infront and then had David Hussey (three) caught in the slip off his last ball of the second over.
Bailey hit a six in the penultimate over before taking a single to seal the match.
Hafeez had dismissed David Warner (five) and Afrridi had Matthew Wade (10).
Earlier left-arm paceman Mitchell Starc took a career best 5-42 and James Pattinson (3-19) to derail Pakistan, who won the toss and batted.
The 22-year-old Starc, who took 4-47 in Australia's 66-run win over Afghanistan here on Saturday, helped Australia keep the lengthy rival batting line-up of seven batsmen to a modest total, losing the last six men for just 38.
Pakistan were recovering well when the batting power-play began in the 36th over with the total at 159-4 but lost three wickets in the five overs for just 16 runs with Starc dismissing Asad Shafiq (56), Kamran Akmal (four) and Shahid Afridi (nought) in an incisive bowling display.
His previous best of 4-27 came against Sri Lanka at Brisbane two years ago. He also took 4-47 in Australia's 66-run win over Afghanistan here on Saturday.
Starc ended all hopes of Pakistan batting through their 50-overs when he had Umar Akmal (52) in the 41st over.
It was Starc's new-ball partner Pattinson who provided Australia with two early breakthroughs, dismissing Hafeez (four) in the fifth over before getting Azhar Ali (five) in the seventh.
Starc forced an edge off a short delivery off opener Nasir Jamshed to wicket-keeper Wade.
Shafiq and Misbah-ul Haq added 59 for the fourth wicket before the Pakistani skipper played a rash shot off paceman Dan Christian and was bowled for 26.
Shafiq then found an able partner in Umar as both hit out at Australian spinners to the best effect, with both hitting two sixes each. Shafiq also hit two boundaries during his 77-ball knock.
Umar also hit two boundaries during his 55-ball knock.
The second match will be played in Abu Dhabi on August 31 while the third will be here on September 3. Both teams will play three Twenty20 internationals in Dubai on September 5, 7 and 10.