The Shrews slumped to a sixth straight home defeat as the Millers tore in to a home side clearly low on confidence with all three goals coming inside the opening 20 minutes.
Striker Tom Hitchcock, on loan from QPR, headed the opener in the ninth minute before Ben Pringle and James Tavernier also weighed in for the Millers.
Evans said afterwards: "I was pleased with the contribution of all my players. It would be difficult to single anyone out as there were a lot of top performances.
"We saw Leyton Orient win here recently and we drove away thinking the only difference between the sides was industry.
"We had to earn the right to play and we think we've got good players but they still have to earn the right to play and I think we did that. It could have been more with the free-kick (from Ben Pringle) against the bar.
"It's very difficult to win away from home in League One and it's a good win for us."
Some of Rotherham's slick attacking play delighted Evans who added: "We work every day on passing and moving. We moved the ball around in the final third and moved defenders around.
"The boys executed that really well in the first half-hour and I think if we had got our rewards it really could have been damage at half time.
"We said second half don't take any chances and keep the ball as we didn't need to force the play."