Duncan Weir also kicked three penalties and Scott Wight one for the Warriors while Edinburgh could only register three from Phil Godman, who also kicked a late drop goal for a losing bonus point.
Weir drew first blood for Glasgow after two minutes with a penalty from 30 metres out while Godman missed with an effort of his own to draw the scores level moments later.
Weir then followed Edinburgh fly-half Godman's lead by failing with a second penalty attempt in the 16th minute before his cross-kick found Alastair Kellock who was denied a try by a great tackle from Lee Jones.
However they were back on the scoreboard shortly after as Weir kicked his second penalty with Godman hitting back for Edinburgh with his first successful penalty in the 23rd minute.
But it was the Warriors who went into the break further ahead as Weir kicked his third penalty of the game to make it 9-3.
Edinburgh struck first after the restart through another Godman penalty but his up and down night with the boot was to continue as he missed with an attempt to pull the scores level soon after.
However he did get another chance in the 58th minute and this time took full advantage but the visitors were soon dealt a killer blow.
Matt Scott was sent to the sin bin for a dangerous tackle on lock Robert Harley with Low credited with a try almost immediately afterwards.
Replacement Wight missed the conversion but he didn't fail with a penalty two minutes later in the 71st minute making it 17-9 which it remained until the death.
Wight missed another penalty and Edinburgh rallied enough for Godman to kick a last-minute drop goal for a losing bonus point and at least something from the defeat.
|Glasgow Warriors Score Card|
|Edinburgh Rugby Score Card|