After running the first half relegation-threatened Wrexham had seen their grip slip before Murray was sent on to open up the right flank.
A half-time lashing from manager Brian Tinnion saw City put a stuttering start behind them and the introduction of Murray for Bradley Orr around the hour proved decisive.
He ran in perfectly to angle Scott Brown's cross from the left past Ben Foster.
Wrexham reacted by sending on Hector Sam to boost their attack but the damage had been done.
The Robins were already heading for a double over the Welsh club and a remarkable unbeaten 11-match run against them - nine of them won.
City, who signalled their intent to rebuild in the summer, had an unfamiliar look both to their line-up and opening half style.
Before the goal they had made just one real chance and that very early on when Paul Heffernan turned past Carlos Edwards to hammer a shot against the bar from the edge of the box.
The rub of the green went against them later when Foster, racing off his line, sent Heffernan tumbling a couple of yards inside his right hand edge of the box.
Both the bench and the crowd rose in anticipation of a penalty call which never came.
Wrexham, their confidence high, after their LVD Vans Trophy success six days earlier, were looking much more aggressive around the box but were being let down by their final ball.
A corner gave them an opening for an attempt at goal as the ball dropped well for Shaun Pejic, but the defender leant back too far and volleyed over the top.
The response from City was a patient raid carefully built for Louis Carey to get in a high cross but promising teenager Scott Golbourne got no power behind the header.