A Marc Richards double in the first half condemned the Millers to a second successive defeat that sees them drop to eighth on 18 points, level on points with Vale who climbed above them into second, and three points below the automatic promotion places.
Rotherham, who were thrashed 4-0 by Southend last week, fell 2-0 behind in quick succession.
Richards drove home from 25 yards on 18 minutes and the just eight minutes later, he latched onto a long kick and a flick on from Williamson to double the lead and leave Rotherham with a mountain they could not climb.
Manager Andy Scott said: “We’ve made two errors, and that’s what’s cost us.
“We were the better side today. We were dominant in that first 15 minutes, but then let a poor goal in, got back into it and then let another terrible goal in.”
For the full report and reaction read Sports Monday, free inside Monday’s Yorkshire Post.