It looked like an achievable total but things soon went awry for the Stars.
Kevin Pietersen (15 from eight balls) could only manage a shortlived BBL return, while Glenn Maxwell’s promotion to the top of the order lasted just three balls before he was bowled by Tom Cooper.
The rain delay proved fruitful for the Renegades, with David Hussey dragging a Hogg delivery onto his stumps on the third ball after the break.
Luke Wright (45) looked to push the run rate and had the Stars well-placed by the time Hogg came back on in the 15th over.
But the 45-year-old spinner struck again, bowling Wright and trapping Sam Harper LBW in quick succession.
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The Stars’ chase ended in comical circumstances with Adam Zampa, Ben Hilfenhaus and Scott Boland all run out in the same over as the Stars fell short on 9-151.
Pietersen earlier threatened to steal the show, taking a spectacular catch to help restrict the Renegades to 4-171.
The former England batsman sprinted 30 metres to take a perfectly timed catch near the boundary and dismiss Sunil Narine.
“I think the whole world knows how much I hate fielding and how rubbish I am in the field,” the 36-year-old said.
“A chance like that, where there’s literally three per cent chance … you just give it a go …”
Veteran Cameron White proved the best contributor with the bat for the Renegades, hitting two sixes on his way to 64 off 43 balls.
Aaron Finch made 30 before being skittled by James Faulkner (1-19), whose disciplined bowling was a highlight for the Stars.
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Last season’s New Year’s Day fixture between the Stars and Renegades attracted a record crowd of 80,883 at the MCG, but the persistent rain dashed hopes this year’s clash would exceed that attendance.