Edinburgh scrum-half Sam Hidalgo-Clyne admits it will take more than a third successive win over Glasgow for the Gunners to claim they are the dominant force in Scotland.
Alan Solomons' side backed up last January's Murrayfield victory with another capital triumph in the opening leg of this year's 1872 Cup duel.
Sunday's 23-11 was another positive indication of the strides being made by Edinburgh - b ut Hidalgo-Clyne believes his club still have some way to go to overtake their rivals from the other end of the M8.
Glasgow became the first Scottish club to win a major trophy when they claimed last year's Guinness Pro12 title.
And since that success they have regularly filled out their new custom-fit 10,000-capacity home at Scotstoun.
Edinburgh, though, continue to attract meagre crowds to Murrayfield - capable of packing in 67,000 supporters - and have struggled to make an impact on the league in recent years.
However, they are on course for a top-six finish this term and could cement their position if they can edge out Glasgow again in the second leg of their annual double header, which also serves as a league match.
Hidalgo-Clyne said: "Glasgow get a lot of hype. They've got their own stadium and are a very settled team. They have worked things out pretty well.
"We're building and trying to get to where Glasgow are but I think as a club we are moving in the right direction.
"That's great and winning these games against them just really tops that off. We had a record crowd on Sunday which was great.
"We are definitely going in the right direction. Glasgow have the stadium and the fan base. We have a big stadium to fill and it's hard to bring fans along to an empty stadium.
"The rugby does the talking and it's the most important thing. We want to make top six this year and we're moving in the right direction now.
"If we were to win on Saturday it would give us bragging rights again. The 1872 Cup is a big thing but we are looking at the league and we can't just judge ourselves on the derby matches. If we finish last in the league and win the cup that's not good for us.
"We really need to be finishing top four and competing for big titles (before we can say we've overtaken Glasgow)."
No Edinburgh side have won in the west since 2003, so it comes as a massive boost for the Gunners that Saturday's return fixture has been switched back to Murrayfield after Storm Frank left the Scotstoun pitch waterlogged.
The capital club take a 12-point lead into the second leg as they look to retain the cup they won last season after ending a five-year wait.
"The important thing is that we backed up last year's win at Murrayfield with last Sunday's victory," said Scotland international Hidalgo-Clyne.
"People said last year that we maybe shouldn't have won that game but for us moving forward it's great for us to have beaten a side who won the title last season.
"It gives us a huge amount of confidence but we can't be complacent. We came back in on Tuesday and had a look at some of the mistakes we made because there was a lot to work on ."