As he did in last weekend's clash in Glasgow, Chris Paterson kicked all of Edinburgh's points - his fifth successful penalty rescued a losing bonus point for Rob Moffat's men in injury-time.
The result saw the Sean Lineen-coached Warriors claim the 1872 Cup title and take the national bragging rights as they opened up a seven-point lead in the table over Edinburgh, who are slipping away from the play-off zone.
Glasgow's efforts at a bitterly cold Murrayfield also bucked the trend in this Scottish derby - the previous twelve meetings between these two sides had all been won by the home side on the day.
Initially Edinburgh showed an improvement on the form they showed in last week's 25-12 defeat at Firhill, but by the end they were well beaten, with Moffat's charges now worryingly four games without a try.
There had been doubts Glasgow would be able to field the planned unchanged side from that which had beaten Edinburgh six days previously, however scrum half Chris Cusiter and hooker Dougie Hall were fit to start.
Instead, it was Edinburgh who were forced into late changes due to a viral infection hitting the camp.
Greig Laidlaw, himself a stand-in recently for Scotland cap Mike Blair, was replaced at scrum half by rookie Ross Samson who was making his Edinburgh debut, while on the bench Jim Thompson dropped out with Steve Jones taking his place.
Glasgow made the livelier start, taking a six-point lead within the first eight minutes thanks to the trusty boot of fly-half Parks, who was making his 100th league appearance just days after becoming the first player to score 1000 points in the competition.
The first score was a penalty awarded after Phil Godman threw out a loose pass with the ball hacked into the home 22. Then, following a lineout in the home 22, man of the moment Parks struck over a drop goal.
Edinburgh were on the back foot but got on to the scoreboard in the tenth minute. Full-back Paterson followed up his own up-and-under to turn his opposite number Stortoni in the tackle and kick the subsequent penalty.
Five minutes later Glasgow confirmed their early superiority with a slick five-pointer. The move began with a Max Evans break through midfield and finished with Parks side-footing the ball to the left corner where Canadian international van der Merwe touched down for the score.
Into the second quarter, Glasgow endured two setbacks when they lost van der Merwe to the sin-bin, after he interfered with airborne Mark Robertson, and just before the break, the visitors' skipper Alastair Kellock saw yellow for tackling Samson early off a scrum.
While Glasgow were without van der Merwe, Paterson and Parks exchanged penalties and Paterson added another, as Kellock watched on from the sideline, cutting Glasgow's lead to 14-9 after some heroic defence had kept the home side at bay.
Kellock had just returned when Glasgow scored their second unconverted try. Richie Vernon forced a five-metre scrum and from the pressure Parks produced a perfect kick for the unmarked Stortoni, who duly touched down.
Glasgow continued to dominate, although Paterson's fourth penalty in the 66th minute kept Edinburgh in bonus point territory.
That seemed to have gone when Edinburgh hooker Ross Ford was sin-binned and Parks added his third penalty just moments later, but Paterson secured some late consolation for Edinburgh with the last kick of the game.
The victory was Glasgow's first away to Edinburgh since they ran out 33-26 winners at Myreside in the Welsh-Scottish League in September 2000.
Speaking afterwards, their coach Sean Lineen said: "There are players playing for positions each week, which is really good, but I am disappointed we didn't get the bonus point.
"I thought we should have scored a couple more tries in the first half.
"Edinburgh didn't really look like scoring. It was quite interesting in the articles during the week, (Edinburgh saying) that when they were back on their wide pitch they were going to run us ragged and score tries.
"Well, a pitch doesn't score tries. It's the players, and we'll take these four points."
|Edinburgh Rugby Score Card|
|Glasgow Warriors Score Card|
|DTH van der Merwe||1||5|