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Davis hooks in opener & Kenny diverts Aribo cross into own goal for second
Edouard penalty saved by McGregor after Elyounoussi spurns glorious chance
Rangers to host St Johnstone in last eight
Hibs beat Stranraer to set up Motherwell quarter-final
Kilmarnock v St Mirren & Aberdeen v Dundee Utd are other last-eight ties
FT: Rangers 2-0 Celtic
That's all for today folks after Scottish Cup wins for Hibs and Rangers.
We have a full Scottish Premiership card on Wednesday, so make sure you join us for that.
FT: Rangers 2-0 Celtic
Celtic interim manager John Kennedy tells Premier Sports: "We were too soft in our pressing, first half, and lacked belief.
"Second half, we reacted well and were on the front foot. But the big chances we had, we weren't clinical.
"In front of goal we didn't have enough belief. When it stays 2-0, you have a mountain to climb.
"Our second half was much better but this game was all about the result, nothing else."
FT: Rangers 2-0 Celtic
Rangers manager Steven Gerrard tells Premier Sports: "I thought we were back to our best. Celtic played their part, it was a really good cup tie. Celtic had their moments in the game but we soaked that up really well.
"We rode our luck at times but I don't think anyone could take it away from us that we deserved it.
"I thought the penalty was really soft. I find it really hard to believe how the referee could give that one."
Rangers now face St Johnstone twice in a week; on Wednesday in the league at McDiarmid Park before hosting the Perth men in the Scottish Cup quarter-final.
Gerrard said: "We won the league really early and from my point of view I've seen the boys come off it, but it was important we made a statement today, we had to be close to our best to beat Celtic and we were. The question is can we maintain it until the end of the season?
"It's important now we treat every game like it's going to be an Old Firm. If we do it'll be an interesting end to the season."
Image source, SNSFT: Rangers 2-0 Celtic
Stuart McCall
Former Motherwell and Rangers manager on Sportsound
Quote MessageRangers were favourites against St Mirren in the League Cup, so there will be no talk of the double, although it will be at the back of their minds
FT: Rangers 2-0 Celtic
Rangers were the last team to beat Celtic in the Scottish Cup, in a semi-final back in April 2016.
The only player involved that day that is still at Ibrox is captain James Tavernier, who returned from injury today to take a place on the bench.
FT: Rangers 2-0 Celtic
Pat Bonner
Former Celtic goalkeeper on BBC Sportsound
Quote MessageDefending has been a major problem for Celtic all season and mentality comes into it. Rangers defend so well as a group
FT: Rangers 2-0 Celtic
Tom English
BBC Scotland's chief sports writer on Sportsound
Quote MessageRangers have a goalkeeper who does things Celtic goalkeepers have failed to do consistently this season - and that's make big saves. Allan McGregor was outstanding.
FT: Stranraer 0-4 Hibernian
You'll be able to see the goals from Hibs' comfortable win at Stranraer on Sportscene too.
Those highlights are already available online.
FT: Rangers 2-0 Celtic
You can catch highlights of Rangers' victory on BBC Scotland at 19:15 BST.
Alan Hutton and Shaun Maloney are the pundits joining host Jonathan Sutherland.
FT: Rangers 2-0 Celtic
Rangers, still unbeaten in the Premiership, will play a quarter-final rehearsal against St Johnstone in Perth on Wednesday.
Celtic must pick themselves up for a visit to Aberdeen, who will have their tails up after a debut win for manager Stephen Glass yesterday.
The Dons are desperate for points as they bid to catch Hibs in third place.
FT: Rangers 2-0 Celtic
Where do Celtic go from here?
Searching for a new manager and in need of a major rebuild, is the simple answer but the task is not so straightforward.
On balance of play, there wasn't much between the sides today but Rangers were clinical, while the visitors were painfully profligate.
Image source, SNSOdsonne Edouard ponders what might have been after his penalty miss
FT: Rangers 2-0 Celtic
Rangers goalscorer Steven Davis tells Premier Sports: "We knew how important it was for us.
"Both teams had chances in the game. In the second half we could have taken better care of the ball, but in the end I think we deserved the win.
"At a club like Rangers questions are always asked of you. We want this title to be the first of many. This is another step in the right direction."
Image source, SNSSteven Davis scored with an acrobatic overhead kick
FT: Rangers 2-0 Celtic
It didn't take long for Rangers to have a bit of fun with John Kennedy's comments from last weekend...
After thrashing Livingston, Celtic's interim boss claimed: "On our day, we are still the best team in the country."
Those remarks immediately generated headlines, with Rangers 20 points ahead with the title already in the bag.
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Remember, the draw for the last eight has already been made.
Here's how it looks, with all of the games coming up next weekend.
FT: Rangers 2-0 Celtic
It's five years and one day since Celtic last lost a Scottish Cup match.
Having completed a remarkable four trebles in a row, they will end this campaign with nothing in the trophy cabinet.
That hasn't happened since 2010.
FT: Rangers 2-0 Celtic
Premiership champions Rangers will be strong favourites to complete a league and cup double now.
The Ibrox side last managed that in 2009.
That's it. Celtic lose their grip on the Scottish Cup, with Rangers rolling into the quarter finals, where they will host St Johnstone.
Steven Davis fired in the opener, with Jonjoe Kenny knocking in an own goal.
Celtic spurned a few gilt-edged chances, with Allan McGregor keeping out an Odsonne Edouard penalty.
Rangers are now unbeaten in five derbies, winning four of those.
Image source, SNSSteven Davis knocked in an early goal for Rangers at Ibrox
Rangers 2-0 Celtic
Celtic are still hunting for a goal but Leigh Griffiths volleys over the top from a tight angle as Allan McGregor fails to deal with a corner.
Rangers 2-0 Celtic
We're into stoppage time now.
Rangers 2-0 Celtic
Celtic sub Albian Ajeti will get five minutes or so as he takes over from Mohamed Elyounoussi, who might well still be thinking of that earlier heavy touch in front of goal.