County gave the men from the Greenyards a scare at Bridgehaugh before their fightback secured a dramatic victory. Melrose's first try came from returning winger Callum Anderson, but they were still 15 points down as the second half progressed.
Fellow winger Damien Hoyland then sparked the comeback with a try and that was followed by efforts from back-row Grant Runciman and centre Joe Helps as Rose edged to a win.
Heriot's and Gala, second and third at the start of the day, also won. The Edinburgh side defeated Aberdeen Grammar 21-18, with converted tries from winger Max Nimmo and centre Max Learmonth putting them 14-13 to the good at the break.
In the second half they could only manage a converted penalty try, but it was enough to see them home.
Gala won 30-8 at Edinburgh Accies, the visitors' four tries coming from stand-off Andy McLean, back-row Stevie Cairns, second-row Craig Borhwick and winger Liam Draycott.
Ayr were on top form to defeat Hawick 48-10 at Millbrae. The visitors were blown away by a great showing from the champions who ran in seven tries.
Winger Craig Gossman began the rout with a converted try after a good break by back-row Graham Fisken and the sides then swapped penalties to make the scoreline 10-3.
Centre Robbie Fergusson then added Ayr's second try after good work from captain Grant Anderson.
Stand-off Ross Curle, later named man of the match, got Ayr's third try to put them 22-3 in front at the interval.
Back-row Andy Dunlop was first to go over for a try after the break before a try double from Scotland Sevens cap Anderson. Following a converted try by Hawick for winger Steven Anderson, Gossman's second of the day rounded things off for Ayr.
Glasgow Hawks won 48-15 at Currie, scrum-half Paddy Boyer leading the way with two tries for the visitors. Five more tries followed, with captain Ross Miller and hooker Finlay Gillies among the scorers.
Winger Harvey Elms and full-back George Horne scored Currie's tries, but they were well beaten.