Rangers progressed to a Scottish Cup clash against Partick Thistle thanks to a Chris Burke strike against Hibernian in the fifth-round Ibrox replay.
Chris Burke fired Rangers ahead in the fifth-round tie at Ibrox
Both teams had early chances but Burke broke the deadlock in 39 minutes, rifling into the corner of the net.
With Hibs chasing an equaliser, Rangers substitute Nacho Novo was red-carded in the 79th minute following a reckless lunge on Thierry Gathuessi.
Hibs rallied in the final minutes but failed to trouble Neil Alexander.
Rangers boss Walter Smith was sent to the stand in the furore which sprung from Novo's ordering off, but the Light Blues held their nerve to keep their four-pronged trophy chase alive.
Smith made six changes from the side which defeated Werder Bremen in the Uefa Cup for the visit of the Edinburgh club.
Goalkeeper Allan McGregor was suspended and was replaced by Alexander, who made his Ibrox debut.
Kevin Thomson, Burke, Steven Naismith, Lee McCulloch and Steven Whittaker were also drafted into the starting line-up.
Hibs also swapped goalkeeper Andy McNeil for Yves Ma-Kalambay for the trip to Ibrox.
An Abderaouf Zarabi foul on Burke provided Rangers with their first real chance of the game.
Thomson played the free-kick quickly to Barry Ferguson, who swept the ball out to Whittaker on the left flank, but his long-range effort was turned wide by Ma-Kalambay.
Whittaker then turned provider when he set up McCulloch for the header but the midfielder nodded just off-target as Rangers attempted to crank up the pressure.
Managers Walter Smith (left) & Mixu Paatelainen clash
Alexander was then called into action at the other end and did well to parry a powerful 30-yard drive from Steven Fletcher.
There was concern for Hibs when Ian Murray was withdrawn for treatment after suffering a facial injury and he was off the park for eight minutes before finally returning to the action.
During his absence, the Light Blues took full advantage of having an extra man when they took the lead six minutes from half-time.
Burke collected a Steven Davis pass from the left before squeezing the shot between two green jerseys, leaving Ma-Kalambay with no chance as the ball nestled in the goalkeeper's right-hand bottom corner.
McCulloch and Ferguson then saw efforts cleared off the line before Naismith's close-range header cracked off the underside of the crossbar.
The Easter Road outfit tried to haul themselves back into the tie after the restart and Murray was not too far away with a thunderous shot that deflected just over the crossbar.
Fletcher then saw a smart free-kick from 25 yards smothered by Alexander at his left-hand post, before fizzing a shot across goal and wide of the upright.
Naismith then had a go at the other end but he blasted well over and Ma-Kalambay was never troubled.
Novo - who replaced Steven Naismith - nearly won a penalty when his cross appeared to strike the hand of Chris Hogg, but Hibs escaped.
Ma-Kalambay had to make an instinctive stop from ex-Hibee Thomson as Rangers swarmed goalward on the counter-attack.
The latter stages exploded when Novo made a crude lunge on Gathuessi near the touchline and referee Craig Thomson ddidn't hesitate to order off the Spaniard.
As a result Thomson also sent Smith to the stand after a clash between the Gers boss and his counterpart Mixu Paatelainen.
The Hibees raced against time in an attempt to conjure an equaliser, but Rangers remained composed to see out the game - while a Scottish Cup success for Hibernian continues to elude them.
Rangers: Alexander, Cuellar, Broadfoot, Dailly, Whittaker, Thomson, Burke, Davis, Ferguson, Naismith (Novo 68), McCulloch (Boyd 81). Subs Not Used: Reidford, Adam, Furman.
Sent Off: Novo (79).
Goal: Burke 39.
Hibernian: Ma-Kalambay, Gathuessi, Hogg, Jones, Zarabi, Kerr (Benjelloun 82), Murray, Rankin, O'Brien, Shiels (Morais 72), Fletcher. Subs Not Used: McNeil, Zemmama, Chisholm.
Booked: Jones, Kerr.
Ref: Craig Thomson