Dean Winnard gave Stanley an early lead but it was the defender's mistake at the other end which gifted Daniel Nardiello a simple equaliser just three minutes later.
Nardiello's near-post cross beat goalkeeper Ian Dunbavin three minutes into the second-half, as the Millers sealed all three points and secured their second away victory in four days.
Evans said: "We have had injuries but players will be coming back over the next three or four weeks and then we will have a great squad going into the second half of the season.
"It was an appalling start as we conceded within two minutes but we came back straight away and in the second half we stepped it up.
"I am happy with the second-half showing. That's six points in two away games."