Sixers, who lost their first six group games and are now on a nine-game winning streak, will meet city rivals Sydney Thunder in Sunday's final.
Hurricanes, led by England's Heather Knight, made 86-8 from 14 overs.
Set 55 from eight overs to win, Alyssa Healy and Ellyse Perry helped Sixers to a 10-wicket win with 10 balls to spare.
The Duckworth-Lewis-adjusted target proved too easy for Australia stars Healy (32 not out) and Perry (22 not out), who raced to their target without loss.
Sixers were also indebted to veteran ex-Australia spinner Lisa Sthalekar, who came out of retirement for this tournament and took 3-9 from her three overs.
She captured the key wickets of captain Knight (16), Erin Burns (26) and New Zealand left-hander Amy Satterthwaite (24) - the only three Hurricanes players to make double figures.
It leaves Sixers all-rounder Laura Marsh as the only England player left in the WBBL, although she did not play in the semi-final and has only featured in six of their 15 games.
Also at the MCG on Friday, Melbourne Stars beat Perth Scorchers by seven wickets in the second men's Big Bash League semi-final, joining Sydney Thunder in Sunday's final.
Sydney Sixers cruised into the inaugural Women's Big Bash League final after beating Hobart Hurricanes in a rain-affected semi-final in Melbourne.