Quinn became the first Kelpies player to transition into league rugby with Grangemouth.
On a good day for rugby, the Stags had the advantage of the considerable Tillicoultry slope in the first half.
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The opening exchanges were fairly even but it was the home side who just about made the most of the play and would eventually lead at the break – although a resolute Stags kept coming back, with Thomas Skelton converting three penalty kicks to keep the score close at 14-9.
The second period followed a similar pattern to the first, with neither side completely in control. Stags managed to score early on before the hosts replied and put Stags under pressure for spells.
With four minutes to play, Grangemouth snatched their second try through Gavin Scott. Skelton converted expertly, unlike a costly miss from the Hillfoots kicker moments before the try, which would prove expensive for the hosts.
In the final moments, Stags held their own in defence and saw out an important win to keep them in fifth spot. They now face a tough trip to face Orkney on Saturday afternoon.