Chasing just 204, Australia crumbled to 6-139 in the 21st over as Rauf skittled the middle-order when the hosts were trying to end the game as quickly as possible.
But captain Pat Cummins (32*), playing his first ODI since last year's stunning World Cup final triumph, was again there at the end in a tight chase as Australia got home with 99 balls to spare.
One of the best quicks of his generation, Cummins has quickly become a specialist run-chaser in the last 18 months after being involved in two close Test wins and three ODI victories.
Rauf (3-67) continued his love affair with the MCG when he breathed life into what had been a straightforward run chase by dismissing Marnus Labuschagne and Glenn Maxwell in consecutive balls.
The 30-year-old was unable to add another MCG hat-trick to the one he took for the Melbourne Stars in the BBL in 2020, but his fiery spell drew roars from the passionate Pakistan fans who made up most of the 25,831 in the crowd.
Australia's shot selection let them down as Matt Short, Jake Fraser-McGurk, Josh Inglis, Labuschagne, and Aaron Hardie all fell in fashion they would be regretting.
Inglis, who has put together an impressive start to the domestic season, threw away a good start after reaching 49.
Hardie (10) inexplicably gave himself room to try to slog the ball to the off-side, but was instead bowled with 25 overs still remaining.
Australia's World Cup heroes Travis Head and Mitch Marsh are on paternity leave and will sit out all three games.
Fraser-McGurk and Matt Short failed to impress as they try to lock down a spot as Head's opening partner ahead of next year's Champions Trophy in Pakistan.
Pakistan only used four bowlers - all quicks - but conceded 21 extras, 17 of them wides.
Earlier, star paceman Mitchell Starc reached 100 ODI wickets in Australia quicker than any bowler, breaking Brett Lee's long-standing record.
Starc removed both of Pakistan's openers - Saim Ayub and Abdullah Shafique - to set the tone for Australia as they bowled the tourists out for 203.
The left-armer - who has the fourth most ODI wickets for Australia, only behind Glenn McGrath, Lee and Shane Warne - began the international summer in ominous form.
Starc - who had a brief period off the field to deal with cramp - nailed his line and length to finish with 3-33 after dismissing Shaheen Shah Afridi (24) in his 10th over.
His 100th wicket in Australia came in his 54th match, going one better than Lee's 55.
With Australia using eight bowlers after Cummins won the toss, legspinner Adam Zampa (2-64) was the only other bowler to take multiple wickets, but went for 18 runs in his 10th over after being hit around the MCG by Naseem Shah.
The Pakistani quick entered the match with just 31 career ODI runs, but smashed 40 in an explosive innings that included four sixes.
Pakistan landed in Australia amid off-field turmoil after respected white-ball coach Gary Kirsten quit his position without actually taking charge in an ODI.
In their first ODI since last year's World Cup, Pakistan struggled to gain any momentum and batted more like a 50-over match in the 1990s.
Babar Azam (37) and new Pakistan white-ball captain Mohammad Rizwan (44) attempted to push towards a competitive total but could never lift the run-rate high enough.
