Hibs had the ball in the net within 13 seconds through Anthony Stokes.
Nacho Novo grabbed a fortunate third for the visitors and Miller's second completed the scoring.
Rangers boss Walter Smith: "Obviously, it's a very pleasing result for us today.
"I felt we played very well after the first 20 minutes or so. I don't think we started the game well but, after that, we played very well and I'm obviously delighted by the result.
"It wasn't just the goal that we lost in the first seconds of the game, in the first 20 minutes of the game we never got the ball down at all and we never imposed ourselves on the game. It took us a while to get going.
"Kris Boyd's been doing exceptionally well for us team-wise. For himself, he's had the realisation that he has to pick himself up a bit and he's doing that and has done for the last three or four months. He's trying far harder team-wise but he's still getting his goals as well, which is obviously the important thing.
"There was a lot of expectation placed on Hibs going in to today's game. We had to work very hard to get our goals today.
"If you look at the game overall, until we got our fourth goal, it was an extremely tough game for us and we had to do exceptionally well to get ourselves in that position."