However, it was Steve Bates' side that took the early advantage with Charlie Hore slotting a penalty in the opening moments.
Edinburgh soon rallied and grabbed a try through former Borders-based forward David Callam. The try followed a reversal of a penalty by referee Neil Ballard following some backchat from the Borders.
They kicked for position and from the ensuing lineout Callam was driven over without much resistance.
The homeside maintained their pressure and a string of Borders' penalties saw the Japan-bound Laney take full advantage with his boot.
Borders showed character to respond before the interval with prop Tom McGee touching down with a little help from his friends following a line-out, with Hore slotting the conversion.
The gap was reduced to a single point 14 minutes into the second half when Hore added another penalty.
But Edinburgh re-asserted their control with first Laney pounces on another penalty to stretch his side's lead.
Then tries from Fergus Pringle, also a former Borders-based star, and another from Callam, both of which were converted by Laney, took the Gunners out of reach.
Borders refused to buckle completely and Jonny Weston crossed for a try after a quickly-taken tap-penalty.
Final score: Edinburgh 31 (Callam 2 try, Pringle, Laney conv, 4 pens), Borders 18 (McGee, Weston try, Hore conv, 2 pen)
|Edinburgh Rugby Score Card|
|The Borders Score Card|