Rangers repeated Sunday's Scottish Cup scoreline against Kilmarnock to keep pace with leaders Celtic.
Craig Moore opened the scoring for Rangers
A close-range goal from captain Craig Moore gave the Glasgow side a deserved half-time lead over the timid visitors.
But they were lucky not to be pegged back after the break, when a curling effort from Garry Hay struck the underside of the home crossbar.
Rangers substitute Hamed Namouchi settled the reigning champions' nerves with a second goal after 76 minutes.
Michael Mols, who came in for the injured Shota Arveladze in attack for Rangers, appeared to havehis shirt pulled by Barry McLaughlin as he tried to turn in the box early on.
But referee Michael McCurry waved play on.
Frank De Boer then saw a header deflected away after he had met a cross from the right from Nuno Capucho.
David Lilley was booked in the 22nd minute for bringing Michael Ball down near the left corner flag and Rangers took the lead from the free-kick.
Fernando Ricksen fired the ball into the box at pace, Ronald de Boer got a flick on and Moore was there at the back post to prod home from unmissable range.
Kris Boyd saw a thumping long-ranger deflected wide for a corner at the other end.
Rangers resumed normal service soon after and Ball sent a rising drive just over before Christian Nerlinger was inches wide with a header.
Emerson was first to check on the injured Capucho
Nerlinger fired wide following a powerful run forward as Rangers threatened after the break.
Danny Invincibile was looking a more potent threat at the other end and he was able to test Klos with a low drive.
Brazilian Emerson, who was given his chance in midfield in place of the unfit Mikel Arteta and was subsequently named man of the match, forced Francois Dubourdeau into a save with a low drive from just inside a crowded box.
But there was a let-off for the home side in the 63rd minute when a corner was only put into the path of taker Garry Hay, who then curled in a long-ranger that beat Klos and rebounded back off the crossbar.
Capucho was stretched off after a Hay tackle and Namouchi scored within four minutes of coming on with a cool finish past Dubourdeau's right hand after he had accepted a defence-opening through-ball from Emerson.
Rangers: Klos, Ross, Moore, Frank de Boer, Ball, Ricksen, Emerson, Nerlinger, Capucho (Namouchi 73), Ronald de Boer, Mols (Ostenstad 66).
Subs Not Used: McGregor, Vanoli, Hutton.
Goals: Moore 23, Namouchi 76.
Kilmarnock: Dubourdeau, Lilley, McLaughlin, Greer, Hay, Fowler, Dodds (McDonald 85), Nish (McSwegan 64), Skora, Boyd, Invincibile (Murray 68).
Subs Not Used: Meldrum, Dindeleux.
Booked: Lilley, Hay.
Referee: M McCurry