Postpublished at 20:19 Greenwich Mean Time 10 March
That'll do us tonight, folks.
Remember Sportscene is on later and we'll be back tomorrow with the final last-eight tie at Cappielow.
G'night.
Listen to Sportsound from Easter Road
Lundstram forces in rebound after Tavernier penalty saved
Obita shown second yellow & Moriah-Welsh gets straight red three minutes later
Silva slides in late second to kill tie
Game delayed after injury to Hibs' Boyle
Rangers join Aberdeen & Celtic plus either Morton or Hearts in Monday's semi-final draw
Nick McPheat
That'll do us tonight, folks.
Remember Sportscene is on later and we'll be back tomorrow with the final last-eight tie at Cappielow.
G'night.
FT: Hibernian 0-2 Rangers
Hibernian boss Nick Montgomery tells BBC Scotland: "Proud of the boys' effort, little bit frustrated with the way the game went and some of the decisions.
"We probably should have scored a goal or two, we limited them to very little. They're a top side. We gave them a real tough game.
"The officials had a bit of a bad day today, but everybody can have a bad day."
On Martin Boyle: "He's landed on his head, probably a bit of concussion, bit of a sore neck and that's something you have to worry about. I'll call him tonight and hopefully get an update."
On the red cards: "I haven't seen Obita's second yellow. I thought Nathan's is really harsh, he's gone across Lundstram. I don't think he really contacted.
"For a strong player like John to go down the way he did... I'm surprised the referee didn't go to the monitor. I'm just bemused by some of the decisions."
Positive news on Martin Boyle.
Hibs have confirmed the forward "is now in a stable condition in hospital" after his clash with John Souttar.
"The winger went straight to hospital after the first-half collision against Rangers and is receiving the best possible care," the club say in a statement.
"The club would like to thank the speed of both clubs’ medical departments in attending to Martin on the pitch."
"Everyone at Hibernian wishes Martin a speedy recovery."
The last of the four quarter-finals.
Championship Morton host top-flight Hearts at Cappielow.
You can watch it live on the BBC Scotland channel from 19:30 GMT.
Still waiting on post-match reaction from Nick Montgomery.
Going to assume he won't be happy with some of the decisions in the game...
FT: Hibernian 0-2 Rangers
Rangers manager Philippe Clement tells BBC Scotland: "It's a massive game to win. We stayed calm and we didn't go into the emotions.
"Everybody worked really hard. We played a mature game in the circumstances. We had a massive game on Thursday that cost a lot of energy. It wasn't easy to come here.
"I'm not thinking about [a domestic treble]. It's game after game. We're two games away from a trophy, but it's two massive games.
"It would be a very massive thing if we can beat Benfica and go through. I think we have one big advantage, and that's our support.
"They will give a lot of energy to the players and that's what we need in this game."
You can watch the best of the weekend action on Sportscene later.
BBC One Scotland at 10:30 GMT.
Rangers join Celtic and Aberdeen in the last four.
The semi-final draw will take place after Monday's quarter-final between Morton and Hearts - live on BBC Scotland.
FT: Hibernian 0-2 Rangers
Kheredine Idessane
BBC Scotland at Easter Road
From a Hibs point of view, they'll regret three mad second-half minutes in which two players hit the self-destruct button to get themselves sent off and completely ruin any chances of their side forcing extra-time.
At 1-0 with 11 men, this was a contest. With nine on the field, Hibs clearly had no chance of stopping the momentum of this Rangers machine.
Still the home side wait for a win over the Ibrox side at Easter Road, something that last happened in 2016.
FT: Hibernian 0-2 Rangers
FT: Hibernian 0-2 Rangers
Billy Dodds
Former Rangers striker on BBC Sportsound
Rangers managed this fixture perfectly after that midweek game, but Hibs will be kicking themselves.
FT: Hibernian 0-2 Rangers
Kheredine Idessane
BBC Scotland at Easter Road
Rangers continue to fight on all fronts after another good performance at a potentially difficult venue.
Their level of consistency and drive, not to mention their reserves of energy, are admirable.
Top of the league, League Cup already won, into the Scottish Cup semi-final draw and in with a very good chance of further progress in the Europa League.
Lots of boxes being ticked as the Clement juggernaut rumbles further forward.
FT: Hibernian 0-2 Rangers
John Collins
Former Hibernian manager on BBC Sportsound
Hibs have played well, they had some good opportunities.
The attitude, the spirit has been good, the confidence has been high, but the final ball has let them down.
Hibernian 0-2 Rangers
League Cup winners Rangers are into another semi-final after dispatching nine-man Hibs.
John Lundstram and Fabio Silva with the goals.
Hibernian 0-2 Rangers
James Tavernier hits the wall then a stunning effort on the follow-up hits Fabio Silva, who is in an offside position.
Flag's up as Cole McKinnon sticks the ball in the net.
Hibernian 0-2 Rangers
Rocky Bushiri trips James Tavernier on the edge of the box and Rangers have a chance to add a third.
Hibernian 0-2 Rangers
Five minutes added.
Hibs want the full-time whistle.
Hibernian 0-2 Rangers
Pass, pass, pass from Rangers.
Nine-man Hibs are chasing shadows.
Hibernian 0-2 Rangers
Kheredine Idessane
BBC Scotland at Easter Road
If the two red cards in three minutes hadn't killed off Hibs' Scottish Cup hopes, that Fabio Silva goal certainly has.
A few folk heading for the exits among the home fans, while the Rangers fans get even louder as they anticipate yet another win and tomorrow's semi-final draw.