The Millers controlled the game almost from start to finish and could have even added to their tally as they moved just outside the Sky Bet League One play-off places.
After Day went off injured at half-time, his replacement Steve Arnold was at fault for the Millers' second as he came out to meet Pringle's free-kick only to be beaten to the ball by Davis.
And the excellent Michael O'Connor put the result beyond doubt when he fired home from 25 yards to round off a superb counter-attack.
Evans said: "It was a good performance, but we've been playing well for a while because there are some good players in that dressing room.
"They'll be feeling tired, but they have a habit of winning football matches when they work as hard as that.
"We were without two or three players here who can also strengthen us as well.
"It was a good performance, but nothing's really changed in the last few weeks because we've been playing well, although maybe the results haven't reflected that.
"When I joined the club 18 months ago, there had to be revolution because it wasn't good enough and now it's about evolution and that's about picking the right players to strengthen the side.
"I thought Claude Davis was brilliant - it took him a few minutes to get going, but after that I don't think he missed a header or a challenge."
Stevenage boss Graham Westley said his players were beginning to feel the strain.
"We can't hang our hat on excuses - what you can see in the 11 players we're trying to win games with is a sense of mental fatigue and maybe physical fatigue," he said.
"We're asking a lot of them by sending the same 11 out game after game after game and it did look like a very fatigued performance.
"Mentally the spark wasn't there and the team spirit that has been so strong in the recent run of results was lacking and there wasn't any energy coming out of the players.
"Don't get me wrong, fatigue is not an excuse but I think it was a factor.
"For the second and third goals, Steve will put his hand up for sure.
"Neither of them were pretty goals from a goalkeeping point of view and they put us out of the game really when the team were struggling and looking fatigued anyway."