However, some strong defending from the hosts ensured that the sides headed into half time level, with neither scoring in the opening 45 minutes.
The Ibrox side continued to look the more likely to score after the break, Little picking out Sandaza with a cross in front of goal, but the ball was just beyond the Spaniard's reach.
The visitors were awarded a penalty in the 70th minute after Lee Wallace was brought down in the box, with McCulloch calmly converting to give Rangers the lead.
Rangers played the last four minutes of the match a man down, after Ian Black picked up his second booking, but the league leaders were able to hold on to take the win.
The result leaves Rangers 20 points clear at the top of the table.