Stars captain Lanning made 71 from 52 balls and Sutherland added 57 from 35 to power their side to 4-192, batting first in the second match of a season-opening double-header at Junction Oval on Thursday.
It was the Stars' highest total at the venue and also against the Hurricanes.
Lanning belted 10 boundaries in her brilliant knock and put on 109 for the third wicket with Sutherland, who smashed five fours and a pair of sixes.
Both eventually fell lbw to Heather Graham (2-31), but not before they managed to put the Stars in a strong position.
In response, Hobart power hitter Lizelle Lee blasted six fours and three sixes in her 57 from 33 balls, before falling to Kim Garth (2-36).
Former Stars captain Sutherland (3-34) and English gun Charlie Dean (1-13) also shone with the ball, helping restrict Hobart to 8-174 in their chase.
"I thought Annabel Sutherland batted incredibly well," Lanning told Fox Cricket.
"We had to soak up a bit of pressure early on and it was nice to see her whack a few around at the back end.
"She's had an incredible 12 months and to see her go out there and play with freedom and show her skills ... she's one of the best players in the world. Hopefully it's just the start for her this year."
In the opening match, Anika Learoyd carved out a career-best innings to lead the Sydney Thunder to a convincing six-wicket win over the Melbourne Renegades.
Learoyd made 48 from 37 balls after off-spinner Georgia Voll (4-26) did most damage with the ball.
In at first drop, after Voll made 25 off 18, Learoyd hit nine boundaries and put on 62 with Heather Knight in a match-turning third-wicket partnership.
Knight (29 not out off 22 balls) and Nadine de Klerk (12no from six) finished the job, guiding their team to 4-140 with 18 balls to spare.
Learoyd admitted feeling "really nervous" batting near the top of the order, but will take confidence from starting the season with a strong performance.
"Probably a little bit of belief, I think," Learoyd told Fox Cricket.
"It's not always something I'm great at, so it's really nice to feel like I can put the scores on the board and hopefully that will help me believe I'm good enough to do it."
Voll's four wickets and hand in a run-out were crucial in restricting the Renegades to 9-138 from their 20 overs.
"She (Voll) was great, wasn't she? The true allrounder," Learoyd said.
"She's been someone who I think is a really good contributor to our group with both bat and ball, and in the field as well.
"It was really nice to see her kick off a really good campaign."
West Indies superstar Hayley Matthews blasted 45 from 30 balls for the Renegades before holing out in the deep.
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