But for their pre-season penalty of a ten point deduction, sixth from bottom Rotherham would have been sixth from top as they faced third placed City.
After a high-energy first half stalemate Delroy Facey grabbed his second goal in two games to give Alan Knill's side the lead five minutes after the restart but Murray levelled after 71 minutes.
City should have grabbed the lead after only eight minutes with their first opportunity. Murray swerved into the area with a powerful run and cut back a neat pass but Scott Brown somehow scooped the ball over from six yards out.
Rotherham did well and worked up their own head of steam as Eugen Bopp hit a long-range effort just wide before Gregor Robertson won the ball and charged forward before curling a super shot that drifted just wide of the top corner.
Bopp seized the chance of shot with a free-kick on 24 minutes but his fierce drive from 25 yards was well held by keeper Adriano Basso.
A minute later a mistake from Bopp and Martin Woods gifted Murray a chance and he curled an eye-catching shot with his left foot but it was matched by keeper Neil Cutler who turned it around the post with a full-stretch save.
Rotherham striker Facey cut in from the right and produced a blistering strike but the angled shot was just off target.
Just before half-time Rotherham saw strong claims for a penalty waved away by referee Peter Walton when striker Will Hoskins tried to curl his shot in but it struck the arm of Liam Fontaine.
Five minutes after the break Facey went close with an effort that would have been a sensational goal when he crashed a 20-yard volley just wide after Hoskins fed him the ball.
And three minutes later it was Facey who made the breakthrough with his second goal in as many matches. Pablo Mills launched a big clearance from the back and when Basso came off his line and hesitated fatally, Facey had the simple task of lifting the ball over stranded keeper.
But then on 71 minutes Jamie McAllister picked out Murray with a long cross-field pass and the winger cut inside cleverly and lashed a tremendous shot past Cutler.