Marvin Andrews and Nacho Novo were on target as Rangers edged past battling Kilmarnock at a rain-soaked Ibrox.
Andrews was on hand to divert a low shot from Stephen Hughes into the net from close range after 10 minutes.
Andrews was denied a second goal by a brilliant double save from Alan Combe, while Kris Boyd came closest for Killie, with a shot that hit the post.
Novo made sure of the points eight minutes from time when he shot home from the edge of the penalty area.
Rangers winger Peter Lovenkrands had the ball in the back of the net in the second minute after a first-time flick from Steven Thompson but the flag was already raised for offside.
Novo tried his luck from 30 yards out with a shot on the bounce but Alan Combe was able to watch it skid wide of his left-hand post.
Rangers went close again when Novo laid the ball back for Thompson to send a low drive from 20 yards that only just missed Combe's other post.
The opening goal came when a corner was cleared only as far as Hughes, who drilled the ball back into the danger zone and Andrews was able to stick out a leg to divert it into the net from inside the six-yard box.
Boyd stole in behind the Rangers defence but fired into the side-netting to waste his side's first chance of the game in the 28th minute.
Thompson sent a glancing header wide then had a much better-placed effort cleared off the line by Craig Dargo.
The second half began with a great 80-yard run from Lovenkrands that saw the winger crowded out in the box at the vital moment.
The Danish international then fired just wide and was only inches away from connecting with Novo's skidding pass across the box.
Combe was behind a Hughes volley after Thompson had flicked the ball up for the midfielder to have a go from 18 yards.
Thompson hit the post in the 58th minute after Novo had slipped the ball to him in the box.
The rebound also deceived Bob Malcolm, who could only scoop the ball over.
Invincible gave the home side a warning in the 68th minute when he sent a thumping 25-yarder into Stefan Klos' midriff.
Andrews was denied when Combe palmed away his back-post header from a Gregory Vignal free-kick and then, having latched on to the loose ball, blasted a fierce drive that the goalkeeper did well to turn over.
Killie's reply was a shot from Boyd that had the beating of Klos but ended up bouncing back into play off his right-hand post.
Rangers extended their lead in the 82nd minute when substitute Dado Prso headed on a Vignal free-kick to allow Novo to run on and smash home the goal that finally killed off Killie and sealed a fifth straight victory for Alex McLeish's side.
Rangers: Klos, Ross, Andrews, Boumsong, Vignal, Ricksen, Malcolm, Hughes, Lovenkrands, Thompson (Prso 79), Novo (Arveladze 83). Subs Not Used: Graeme Smith, McLean, Kalenga, Davidson, McCormack. Goals: Andrews 10, Novo 82. Kilmarnock: Combe, Fowler, Lilley, Dindeleux, Leven, Invincibile, Locke, McDonald, Johnston, Boyd, Dargo (Nish 78). Subs Not Used: Smith, Greer, Dillon, Murray, Dodds, Canning. Booked: Boyd, Fowler, Locke. Att: 46,278 Ref: I Brines