Three wickets from Mitchell Starc saw the Lions restricted to 137 for nine from their 20 overs, with Gulam Bodi topscoring with 61 from 44 balls.
Aaron Phangiso took three wickets for the Lions, but the Sixers reached their victory target with six balls and five wickets in hand with Shane Watson scoring 47 and Haddin 32.
It was the Sixers’ third successive win in Group B and sees Brad Haddin’s side top the standings with 12 points on the board.
The Lions remain second in the group with eight points, with Mumbai Indians and Yorkshire to meet in the day’s second encounter.
Rain washed out Yorkshire's second group game against Mumbai Indians with the Indian side in a strong position.
Dwayne Smith hammered 37 from 26 balls, with four sixes, and fellow West Indian Kieron Pollard added 37 from 20 as Mumbai reached 156 for six with 13 balls remaining in their innings before heavy rain ended the contest.
- Mitchell Starc