Rnagers are 45 minutes away from the fifth round of the Scottish Cup after taking a 1-0 lead in at half time against Kilmarnock at Ibrox.
Lee McCulloch perhaps should have done better when he flashed a near-post header over the bar from a corner on 14 minutes.
Alexei Eremenko almost gave Kilmarnock the lead when his low effort was deflected into the side netting shortly after McCulloch's chance.
Rangers had a penalty appeal waved away when the ball appeared to strike Tope Obadeyi on the hand, but moments later the home side were ahead.
The ball dropped to Nicky Law on the edge of the box and the 26-year-old curled an effort into the corner via a headed deflection off a defender.
Lewis Macleod unleashed a left-footed volley from 25 yards out shortly before Kenny Miller was denied by a vital last-ditch tackle inside the area by Ross Barbour as Kilmarnock ensured that the deficit would just be one at the break.
Paul Gorst
