Aamir's patient 52 helped Pakistan overhaul Australia's 199 all out to reach 203 for 6 with 27 balls to spare at the Sydney Cricket Ground.
The left-arm orthodox spinner had earlier removed Greg Blewett for 33 and Paul Reiffel for three as Australia laboured to master Pakistan's spin attack.
After taking 2 for 33 from his nine overs, Aamir added 54 runs in a brisk opening partnership with Shahid Afridi.
WORLD SERIES (Sydney): Australia 199; Pakistan 203 for 6 (Ijaz Ahmed 58, Aamir Sohail 52). Pakistan won by four wickets. Standings: 1 Pakistan (P3, Pts4); 2 Australia (4-4); 3 West Indies (3-2).