Mumbai bowlers stuck to their task with pacers Lasith Malinga and Munaf Patel picking up a couple of wickets each.
Barring a few overs at the start, Mumbai bowlers put up a splendid show to stop Big Bash winners from posting a challenging total.
Steven Smith top-scored for Sydney with a run-a-ball 41 and together with Nic Maddinson (27) added 36 runs for the fourth-wicket partnership, which was the only highlight of the Australian team's innings after the good start given by the openers.
Electing to bat, Michael Lumb and Peter Nevill provided Sydney Sixers with a solid start but Munaf's twin strike in the sixth over pegged the Australian team back.
Malinga struck to give Mumbai first breakthrough having Lumb (28) caught by Dwayne Smith at deep midwicket. Lumb added 33-run for the opening stand with Nevill.
In the next over, Patel's double strike reduced the Sydney side to 40 for three in 5.3 overs and turned the momentum in Mumbai's way.
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Munaf first accounted for Nevill, who mistimed a pull shot only to find Thisara Perera at mid-on. Two balls later, Haddin departed without troubling the scorers as he was caught by Ambati Rayudu at cover-point while trying to play a cut shot. Munaf's third over was a double-wicket maiden.
Sydney struggled to build any substantial partnership after the departure of their openers as they lost wickets at regular intervals.
Maddinson and Smith tried to revive the innings before the former got run-out by Malinga. Maddinson's 13-ball knock included a couple of boundaries and an equal number of sixes.
Skipper Harbhajan Singh piled more misery on Sydney as he scalped Moises Henriques (0) to leave Sydney tottering at 77/5 in 12 overs.
Towards the end, Nathan McCullum scored an unbeaten 12-ball 20 to help his side reach a modest total.