Miller told Sky Sports: "The performance was different class. The lads at the back saved us a couple of times and I thought it was a tremendous performance by the team.
"We need to build on this win. This is a game where all the fans and everybody (at the club) gets up for it. We need to play well against the teams in and around us in the league and hopefully we can climb the league."
The Dons had to play the last 30 minutes of the match with 10 men after Mark Kerr was sent off for a second yellow card.
"It was a bit soft the second booking, I didn't really see the first one," Miller added.
"Mark has been different class this season and we will miss him."
Aberdeen goalkeeper Jamie Langfield played his part with a crucial save from Kris Boyd and said: "It was one of those instinctive things, I just threw a hand up.
"I was actually waiting for the linesman to flag up for offside. Hopefully it made up for little blip I had last week and it's great to get the three points, especially against Rangers. All credit to the boys, I think we deserved the three points."