The Edinburgh school made sure of victory at Murrayfield with a strong performance which was built on their opening try in the sixth minute from back-row Benjamin Kenderdine.
They doubled their advantage to 10-0 in the 47th minute when fellow back-row Jamie Maran scored, and then survived a late onslaught from Strathallan.
Scrum-half Nutton, who put in a good showing only marred by a second half yellow card, said: “This is what we have been building for all year and to come out on top at the home of Scottish rugby is just amazing for us all.
“It was good to get the early try because it settled us down and put Strathallan on the back foot. Credit to them, though, they came back strong and we had to dig deep in the second half, but we got there and it is awesome to have a winners’ medal.”
Merchiston did come out of the blocks quickly and Kenderdine’s try was just what they deserved early on.
Strathallan then had a lot of possession as they tried to get back in to things, but the Edinburgh school’s defence did well to keep their quick backs at bay, and it was 5-0 at the interval.
Twelve minutes after the break, the Merchiston second try arrived through Maran. Strathallan then scored a try though through Alfonso Ramos and when Nutton was yellow carded it sparked a frantic finale.
Strathallan: C Nicol; J Rutherford, H Tyson, C Holborn, H Thomson; J Henderson, P Rumble; R Muir, J Waller, H Manos, F Buchan, A Ramos, C Hirst, J Burdett, G Meiklem. Subs: L Steele, M Chan, S Taylor, W Dallas, F Stewart, D Cook, C Gordon.
Merchiston Castle: J Gillan; A Ogilvy, T Harvey, T Bissett, A White; F Ellison, D Nutton; G Tarr, H Burn, J Lascelles, S Richardson, A Middleton, J Maran, B Kenderdine, K MacCormick. Subs: A Evans, T Henderson, M Oliver, J McDonald, L Baird, H Ellis, L Tang.
Referee: S Grove-White.