Port Vale turned on the style in the 23rd minute after doing little else before when Stefan Moore's back-heel on the edge of the box set up Richie Humphreys for a volley that zipped over the bar.
The Valiants started to command more possession as the half went on but struggled to turn it into goals with Neil Cutler being given another comfortable save from Danny Whitaker after 36 minutes.
Things heated up five minutes before the break when, after a seemingly harmless nudge by Richard Walker on Dave Hibbert, the former Vale striker looked to spit in the defender's direction.
Rotherham almost grabbed a goal in first-half stoppage time when Scott Wiseman delivered a great cross but Will Hoskins' header was well caught by Mark Goodlad down to his right.
The Millers took the lead only two minutes into the second half when Michael Keane's curling cross from the left found the head of Cochrane and he sent the ball looping into Goodlad's top left corner.
The home side were given a lifeline in the 74th minute when Scott Wiseman was caught pulling the shirt of Walker inside the area by eagle-eyed referee Darren Drysdale.
Sub Leon Constantine stepped up to the spot and confidently stroked the ball into the bottom left corner of Cutler's goal.
The victory sees the Millers close the gap on Orient at the foot of League One, whilst Vale remain in 8th spot just short of the play off pack.