Penalty goals were the order of the day in the first half at Firhill, with a fourth successful effort from Edinburgh full-back Chris Paterson reducing Glasgow's lead to 15-12 for half-time.
But, by the 54th minute, the Warriors had crucially stretched their advantage to 13 points. Vernon's seven-pointer and Parks' fifth penalty strike left Edinburgh, who were wearing their colourful special edition jerseys, with a mountain they just could not climb.
The result took Glasgow's unbeaten league run to five games ahead of next weekend's return fixture at Murrayfield.
Sean Lineen's charges dominated for the most part from the third minute onwards, when Parks' kick to the corner set up the field position for his first penalty.
His Scottish international colleague Paterson equalised a couple of minutes later but, in the 11th minute, the crowd rose to applaud Parks' second penalty which meant he became the first player to reach 1000 points in the Magners League - 1001 to be exact.
The official attendance, which was just shy of the 9000 mark, was a record for a Glasgow home match.
With all the territory and possession, Glasgow still had to rely on the boot of Parks to keep them in the lead, four first half penalties and a drop goal taking the fired-up home side in at the break with a 15-12 buffer.
Paterson was Edinburgh's only scorer in the opening half, with four penalties from four attempts. His last two came after the two opensides, John Barclay and Roddy Grant, were sent to the sin-bin on 29 minutes for getting involved in an altercation as tempers started to fray.
Glasgow came closest to breaking the try deadlock in the opening half, but television match official Jim Yuille ruled that home prop Jon Welsh had not grounded the ball sufficiently for the score. Richie Vernon and Thom Evans were also denied by some determined defending from the visitors.
David Callam and Scott Newlands stood out in that regard, putting in some thumping tackles for an Edinburgh side looking to continue their enviable away form in the league - they had won five of their last six matches on the road.
But their defence gave way, ten minutes into the second half, when key man Vernon used scrum ball to attack and spin out of a couple of tackles before muscling his way over the line for a decisive try which Parks converted from the touchline.
Parks' fifth successful penalty, which took his league tally to 1015 points, added further cushion to Glasgow's lead before Edinburgh staged a late rally.
Pounding the Glasgow line for 10 minutes however brought nothing for Rob Moffat's men as John Barclay, Vernon and Kelly Brown kept the home whitewash intact.
A Paterson penalty miss, 10 minutes from the finish, summed up Edinburgh's afternoon and Glasgow's solid defence saw them hold firm for a well-deserved festive win.
Speaking afterwards, Glasgow coach Lineen said: "It wasn't a pretty game but derbies rarely are. It's all about winning and both teams got stuck in.
"We could have put a few more points on the board but I'm really happy with the result.
"The banter between Edinburgh and Glasgow is always good and the guys just wanted to make a statement.
"They will come out all guns blazing (in the return leg next Saturday) and there were a few verbals straight after the game."
|Glasgow Warriors Score Card|
|Edinburgh Rugby Score Card|