Edinburgh delivered a "complete performance" and "outplayed Glasgow in both games" to retain the 1872 Cup, believes head coach Richard Cockerill.
The visitors prevailed 16-8 at Scotstoun to back up their 23-17 win at Murrayfield over their Scottish rivals.
"We play how we play, love it or hate it," Cockerill said. "We played good rugby in the first half, put them under pressure, we didn't let them settle.
"And our set-piece was unbelievably good. They just couldn't cope with it."
Cockerill told BBC Scotland his side had taken their lead from English champions Saracens, the only other side to win at Scotstoun - in the European Champions Cup pool stages - this season.
"I get a bit fed up when I hear that last week it was all about how poorly Glasgow played," said the former England hooker.
"There are two sides that have won here - Edinburgh and Saracens. That is blooming good company to keep. We worked hard and deserve lots of credit because we outplayed Glasgow in both games, home and away.
"They are a great side if you let them play, but if you don't let them play they are going to be under pressure. We watched the Saracens game and it was a great blue-print for us to follow. We did it pretty well.
"It is a big step in the right direction for us. Everyone expected Glasgow to come out all guns blazing and knock us over and restore the order. So psychologically this is great for us."
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Cockerill added he will rest some players for next Saturday's home league game against Southern Kings, who are bottom of Conference B with only one win all season, before Edinburgh resume their European campaign at Toulon in a fortnight.
Hogg suffers fresh injury blow
Warriors also have a Pro14 game to negotiate - away to Benetton in Treviso - next Saturday and neither Stuart Hogg nor Alex Dunbar are likely to be involved, before Glasgow host Cardiff Blues in the Champions Cup on 13 January.
Head coach Dave Rennie revealed full-back Hogg was forced off at half-time with "a bit of a groin/hip issue", adding: "I'm not sure where he'll be at regarding the next week or two".
Fellow Scotland international Dunbar limped off with a leg injury - "a bit of a haematoma or something", Rennie reported, "but I don't think anything too major".
The New Zealander blamed a "lack of accuracy" and his side's failure to "hang onto the ball for long enough" for their defeat.
But he also admitted his frustration at referee George Clancy's interpretation at the scrum, where Edinburgh won a string of penalties.
"Last week they walked around the scrum and they got rewarded for it, so good on them, they keep doing it," he told BBC Scotland.
"We found out during the week that the referee got it wrong and they are seeing about sorting it out, and then we get exactly the same picture first scrum tonight.
"If it's not sorted out then basically every team will start walking left and we're going to end up with a mess and we'll never get any footy played off it. When they're forced to push straight, you get good scrums and you get a contest.
"But I'm not looking to blame the ref for tonight. We weren't good enough and we've got to look at ourselves."
'Edinburgh have got the hex on Glasgow' - Analysis
Former Edinburgh and Scotland centre Scott Hastings on Radio Scotland:
"Edinburgh played extremely well. They've based their game on great structure, superb defence and a real willingness to take Glasgow on up front and put them under pressure in both these games.
"Richard Cockerill has completely revolutionised Edinburgh Rugby and what their values are. He's made sure they have started to believe in themselves."
Former Glasgow and Scotland prop Peter Wright on Radio Scotland:
"I thought Glasgow were poorer this week than they were last week. They had so many unforced errors, turnovers at the wrong times, and the set-piece was a disaster.
"I think Edinburgh have got the hex on them. At home you always expect a performance from Glasgow, but this was their worst performance for a couple of seasons. Edinburgh's squad is not as strong, but their starting 15 is better, as has been proven in the last two games."