The visitors could muster just 73 runs, gifting the home side a comprehensive 68-run win.
Auckland will play Canterbury in the final and shapes as the favourite after its convincing display.
The Hearts posted 141 for five. Opener Samantha Curtis scored an undefeated 69 at the top of the innings. Maddy Green chipped in with 29 and Katie Perkins added 21 not out.
Sparks captain Suzie Bates was the best of the bowlers with two for 22. Leigh Kasperek also picked up two but conceded 36 runs.
Otago's reply unravelled quickly when Bates (1) was trapped lbw by Holly Huddleston in the opening over.
The right-armer struck again quickly, removing the dangerous Sarah Tsukigawa (10) before she could get going. Kasperek did not trouble the scorer and neither did Polly Inglis. Millie Cowan managed five before she joined her team-mates on the sideline.
At 35 for five, the situation was bleak and only got worse when Katey Martin offered a catch on 22.
Spinner Georgia Guy took three for 17 from her allotment of four overs.
Otago can make amends for the limp performance with a win against Auckland in one of the back-to-back one-dayers this weekend. The Sparks lead the one-day tournament and need one win to cement a final spot.
