The contrasting fortunes of the goalkeepers had a significant say in proceedings in Dingwall.
Rangers' Jack Butland stumbled on the ball and County could not take advantage.
He regained his composure, with a deflected Noah Chilvers effort at 1-0 and the second Wright header bringing out the best in the England international.
When Hamilton, who has stepped in for the injured Ross Laidlaw, took a heavy touch before an attempted clearance, Danilo pounced, charging down the ball and chasing in to add a simple finish.
The stand-in goalkeeper twice did well to foil Vaclav Cerny and Nedim Bajrami but had other nervous moments, including a misunderstanding that almost caused an own goal off Eli Campbell and spilling a second-half corner.
However, Hamilton could do nothing about Igamane's strike from the left looping over him, nor Tavernier's swerving shot when County were caught short at the back.
And his manager Don Cowie said afterwards: "Jack had done really well up until that point in the game. Maybe he just got caught out slightly in terms of the tempo of the game. We're not going to get caught too much up in it. For the majority of today, he did really well."