Stirling were first to get the scoreboard moving when they were awarded a penalty try following a period of sustained pressure on the visitors’ line.
Melrose hit back when the ball was spun out wide to Ian Sim who sprinted in at the corner, Struan Hutchison converting.
The pendulum swung back to Stirling when George Arnott finished a quick break, Andrew Goudie adding the extras, but Melrose had the final word of the first period when Patrick Anderson touched down.
Controversy marked the start of the second half when Melrose lock James Head was red-carded but Hutchison nudged the visitors in front with a penalty.
An Angus Runciman try, converted by Hutchison, extended the lead and a late Ratu Tagive try proved not enough for the home side to snatch a win.