The Sixers beat the Hurricanes by seven runs, despite Hobart being well placed at 0-98 after ten overs.
The Hurricanes lost 4-4 in the last two overs as the match slipped away.
Sixers captain Steve Smith (52 off 32 balls) inspired his side with a typically well paced innings and a crucial catch to dismiss Travis Birt (33 off 21), who threatened to win the match for the visitors at the end.
The win lifted Sydney level on points with second-placed Perth and left fourth-placed Hobart in a vulnerable position.
Wicketkeeper-captain Tim Paine (57 off 30) and Ben Dunk (39 off 35) got the Hurricanes off to a breakneck start, racing to 50 off 26 balls.
Spinners Nathan Lyon (2-28 off 4), Stephen O'Keefe (1-33 off 4) and Marcus North (1-7 off 1), hauled the Sixers back into the contest.
Josh Hazlewood (2-25 off 3) took the wickets of Birt and Evan Gulbis (7 off 8) of successive deliveries in the 19th over and almost completed a hat trick when Ben Laughlin skied the next ball between some fielders.
Needing 13 off the final over, Hobart lost the wickets of Shoaib Malik and Laughlin.
Smith and Jordan Silk (32 of 27) added 77 off 48 balls to help lift the Sixers to 6-179 after they slumped to 4-88 after 11 overs.
Experienced paceman Ben Hilfenhaus (2-25 off 4 overs) conceded 11 of his first over, but helped drag the Hurricanes back into the contest after the early Sixers onslaught.