After a sluggish start to the tournament, D'Arcy Short was shifted down to No.3 for Hobart, breaking his long-time BBL combination with Matthew Wade.
McDermott launched four maximums, including one off Nathan Coulter-Nile that cleared the Bellerive Oval hill and ended up in a backyard.
He fell in the 14th over caught in the outfield off Andre Russell.
The Hurricanes were sensationally hit with a five-run penalty, meaning the Stars will begin at 0-5, after Tim David was called for deliberately running short in the final over.
David was trying to run two but grounded his bat about two metres away from the crease on his return.
McDermott put on a 93-run opening stand with Wade (39 from 27) after Hobart won the toss and elected to bat, before the skipper fell in the 10th over to Coulter-Nile.
Short was six off ten balls at one stage but briefly came to life with back-to-back boundaries and a maximum in the space of three balls off Russell.
He was out off a high-leading edge for 26 off 24 deliveries off the West Indian in the 17th over.
Short had 138 runs under his belt coming into the game but has struggled to get going during the opening powerplay.
Coulter-Nile finished with an impressive 2-22 off four overs, with the Hurricanes middle order not fully capitalising on the quick start.
The Stars are without legspinner Adam Zampa, who is being rested, while Joe Burns is playing his first match for the tournament at the expense of Nick Larkin.
Hobart have won just one match from four and are second last on the ladder, while Melbourne have won two from four.