The Millers breathed further life into their fight against Sky Bet Championship relegation with a superb 3-0 victory over the Robins - their biggest at this level since 2004 - which moved them to within a point of safety.
It came on the back of last week's success at Leeds and heading into a run of fixtures that on paper looks favourable, confidence at the New York Stadium is growing.
Clarke-Harris' double and Lee Frecklington's late strike ensured the Millers found the net three times for the first time since February, but it was at the other end where Redfearn was happiest.
The thought of back-to-back clean sheets seemed a million miles away after the horror show against Ipswich at the start of the month, but experienced heads have made the Millers a harder nut to crack.
“It’s good to score three, but, to be honest with you, and I know it’s a really boring thing to say, I’m more pleased with the clean sheet. The clean sheet is everything," Redfearn said.
“Bristol City are a side who have got some results recently and to ‘nil’ them is no mean feat. There was a little bit of luck in there. But I’ve always been told that the harder you work, the luckier you get, and we worked our socks off.
“It’s a couple of wins. It’s a long, old season. I think the presence of some experience has helped. If you look at the back four, it’s a really experienced back four with Danny Collins at left-back. It’s given us a platform.
“Now, when games are tight and there isn’t much in them, like at Leeds last week, we look mentally tough. We look strong."
