The Millers trailed to a first-half strike from Ashley Grimes, but dominated the second period and deservedly levelled through Kayode Odejayi's 76th minute effort.
And Aston Villa loanee Courtney Cameron fired the winner in the 90th minute to sent Evans men up to third in the table.
"The winner came in the last minute of the match, but I thought we were very unlucky to go behind in the first place," said the Rotherham boss.
"We were disappointed with the goal we conceded but we told the players we believed in them and credit to them.
"There's not a lot of clubs at our level who went away together on New Year's Eve and kept their players from temptation, but I told them over the course of the season that if you show that kind of professionalism over the season you will get your rewards, and we did today.
"This squad has great character - we were decimated by injury at the start of the season. This is a really tough place to come.
"I brought in the new year watching the DVD of their game at Bradford on Saturday and they were totally dominant. We had to counter that, and this was a really hard earned three points because John Coleman is starting to stamp his mark on Rochdale.
"From the first whistle in the second half it was almost total domination, so the win was thoroughly deserved."