With captain Matt Short top-scoring with 56 from 42 balls, the Strikers posted 8-155 as Stars quicks Harris Rauf (3-28) and Tom Curran (3-35) claimed three wickets each.
The Stars' Harper struck 55 from 36 balls as they chased down the target at Adelaide Oval on Tuesday night with 11 balls to spare, reaching 4-161 to bank a second consecutive win to open their campaign.
The Stars' usual opener Tom Rogers couldn't bat after injuring a shoulder in the field.
But Harper and Joe Clarke (23 from 19) set an ominous tone, smacking 50 runs from the initial 24 balls.
The Stars' openers reached 67 before the partnership was broken when legspinner Lloyd Pope (1-22) bowled Clarke with a wrong'un from the top shelf on the last ball of the seventh over.
Harper posted his half-century from 35 balls but was dismissed next ball when skying to mid-on from the bowling of Jamie Overton (1-39) in the 10th over.
The visitors were at a comfortable 2-90 at the halfway stage but lost Glenn Maxwell (two from four balls) cheaply.
Campbell Kellaway (28 from 22) and Marcus Stoinis (32no from 22) - who hit a six to win the game - ensured there were no following hiccups.
Earlier, the Strikers' innings was rocked by a double blow in the second over when Stars paceman Curran snared two wickets in three balls.
Curran bowled veteran Chris Lynn (four off four balls) with an off-cutter through the gate and then produced a superb leg-cutter which clipped the off-stump of Jason Sangha, who failed to score.
Short and Liam Scott steadied, registering a 50-run stand from 34 balls and taking the total to 62 in the eighth over.
Stars allrounder Marcus Stoinis (1-23) ended the union when Scott (25 from 19) was trapped lbw and, soon after, Short was given a reprieve on 40 when a hesitant Tom Whitney turfed a simple skied chance at cover from Curran's bowling.
At their midpoint, the Strikers were 3-83 and Short soon after posted his half-century from 38 balls.
But just when the skipper was set to wind up, he smacked a Curran delivery to extra cover where Stoinis took a sharp catch with both arms outstretched above his head.
Short's departure left Adelaide 4-110 in the 14th over and the home side couldn't gain any late traction with Rauf taking two wickets in consecutive balls in the 19th ove
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