The heavy and treacherous surface and the wet overhead conditions made it all but impossible for the game to be played with the skill and pace both teams have shown in the earlier rounds and for the most part, save for one brilliant and ultimately winning move by Stewart's Melville, it was a forward slog out of which the visitors emerged the better.
"We used our forwards well in the second-half," said Chris Spence, the visiting coach.
Flanker Ben Johnstone led an inspired back row, while at the heart of matters George Turner, viewed as a hooker at representative level but playing on the tighthead on Saturday, contributed immensely.
On a day when there was little opportunity for the backs to show their skills, Andrew Warnock of Stewart's-Melville posted a useful performance, but it was his opposite number, Sam Hidalgo-Clyne, who had the greater controlling influence.
Merchiston, however, failed to capitalise on their stand-off's territorial gains and their coach James Boyd admitted: "We didn't threaten them in their own 22-metre area. They took their one opportunity to score; we didn't take ours."
Merchiston led 3-0 at the break from a Hildago-Clyne penalty but it was the visitors, reduced to 14 men after centre Alistair Hagart was shown the yellow card, who finished the first half the stronger.
Encouraged by their pre-interval performance, the Stewart's- Melville pack gradually edged ahead in the forward battle and from a scrum on the Merchiston 22 the visitors produced their winning score, stand-off Warnock looping round centre Mike Crawley to score under the posts, leaving him with a simple conversion kick.
Merchiston tried desperately to claw back the points but despite a clean break from Hidalgo-Clyne they were unable to break down the visitors' defence, and it was Stewart' s-Melville who marched on to Murrayfield.
Scorers: Merchiston: Penalty: Hidalgo-Clyne. Stewart's-Melville: Try: Warnock. Conversion: Warnock.
Merchiston Castle School: H Clark; G Skivington-Jones, M Paterson, J Nutton, M Jackson; S Hidalgo-Clyne, M Watson; M. Roger D Muir, G Wilson, D Morrow, J Jones, P Baker, A White, D Muir. Subs: A Paterson, D Duff, F Donaldson.
Stewart's-Meville College: S Cook; A Hughes, A Hagart, M Crawley, M Batchelor ; A Warnock, J Gilfillan; M Campbell, J Cook, G Turner, B Docherty, R McPhail, N Bowie, B Johnstone, A Wilson. Subs: C Taylor.
Referee: A McMenemy (Gala).