Key events
Paul MacInnes' report from Ibrox is here. Thanks all for tuning in.
Rangers will face Aberdeen in the semi-finals, with Hearts taking on Hibernian. The ties will take place on the weekend of 31 October and 1 November.
James Penrice was another who looked the part for Rangers, crossing for the second goal and whipping in for the one that was disallowed. Really, though, Rangers were just excellent across the board.
Dan Neil is the matchwinner with his brace, but I was particularly impressed by Djeidi Gassama over on the left for Rangers, causing all sorts of havoc. Celtic, with no support in the stands, looked off it from the start.
Rangers head to the semi-finals; Celtic are beaten domestically for the first time this campaign.
FULL-TIME: Rangers 3-0 Celtic
It's not been much of a contest. Derek McInnes triumphs comprehensively in his first Old Firm derby in charge of Rangers.
90+3 min: The ball is trapped near the corner flag as we wait for the inevitable.
90+2 min: We've got four added minutes.
90 min: Hassan has been a bit of light for Celtic in this half – he drives down the right and sends in another dangerous cross. Moments later, he cuts in from the left and repeats the trick.
87 min: Kelsy leaves the field, too – his goal was calmly taken and he's been the focal point for Rangers, something Celtic have lacked today.
85 min: Gassama and Neil, both sparkling today, are taken off. The fans show plenty of love.
84 min: A silly foul from Fernandez, about 30 yards from goal … but Celtic's free-kick causes no real bother.
82 min: Gassama is hauled down by Donovan, on a yellow, inside the Rangers half.
80 min: Celtic have been particularly poor this half. In the first, at the very least, they threatened to do something on the counter.
77 min: Time for a brawl between both sides, over on the Celtic right wing. It's after Sterling hauls down Hassan, with Penrice then kicking the ball at the Celtic winger. Penrice and Hassan are both handed yellows.
This is some finish from the Rangers captain, picking the ball up inside the D once again. This time he curls it into the top right corner, Johnstone standing no chance.
GOAL! Rangers 3-0 Celtic (Neil 75)
That'll seal it.

74 min: Min-su goes off for Rangers, with Badredine Bouanani on.
72 min: Hassan cuts in from the left and launches … wide of the Rangers goal. Pandur's barely had to do anything this half.
70 min: Penrice sends in a dangerous corner – his delivery's been excellent all day. A cross in from the other side very nearly threatens to go in on its own.
69 min: The electric Gassama drifts down the left and dinks a ball in … it's headed away for a corner.
68 min: Alex Oxlade-Chamberlain has come on for Celtic and twists and turns in midfield to win a free-kick.
67 min: Celtic are parked inside their own half, Rangers' move breaking down with a wayward Fernandez shot.
DISALLOWED GOAL!
Penrice's ball finds Fernandez, who heads in! But the flag goes up and Celtic are, just about, still in this.
63 min: Gassama is fouled on the left and Penrice has another chance to whip in a cross …
We've got a check for offside … but it's all clear, allowing Rangers fans to celebrate once again.
Penrice crosses from the left, the ball is nodded to the far post, and Kelsy is a free man. He's calm under the dropping ball, his volley finding the bottom right corner. Again, it's a goal that's been coming.
GOAL! Rangers 2-0 Celtic (Kelsy 59)
Ibrox erupts once again.

58 min: Here's some space for Hassan over on the right … but he finds traffic when cutting into the middle. Rangers drive down the other end, the ball breaking for Min-su inside the area … Johnstone rushes out to close the angle and make a fine save.
54 min: Celtic haven't changed much since the break; Rangers remain in control here.
53 min: The impressive Naderi wins the ball in midfield to get Rangers moving … Raskin whips in a cross, searching for Kelsy, but he can't get in the right position to head at goal.
52 min: Fernandez launches from 25 yards out … and the ball travels to the stratosphere.
50 min: Corner for Rangers … Naderi heads from beyond the far post, but Johnstone collects fairly comfortably.
48 min: Min-su finds space outside the area and lasers a drive … Johnstone makes a strong save, moving to his right. That'll be a nice boost for the Celtic keeper, who had a tough first half.
47 min: Hassan's danger is evident, driving down the right again as Makhanya takes him down. Yellow card for the Rangers centre-half.
46 min: Hassan is immediately into the action, jinking down the right and getting a cross in.
A half-time change for Celtic. Haissem Hassan replaces Tounekti, with Durán moving over to the left wing.
Rangers' goal came from some neat buildup down the left, where Celtic have really struggled. Djeidi Gassama hasn't brought the end product just yet, but he looks dangerous when cutting in or going on the outside. The key strike came from Dan Neil, his very first goal for the club.
HALF-TIME: Rangers 1-0 Celtic
Martin O'Neill's got a few problems to solve at the break.
45 min: Min-su crosses low from the right … but it's out of Kelsy's reach. We'll have an extra minute.
44 min: Neil picks out the energetic Gassama down the left … but the flag goes up. Celtic have a real problem to sort down their right-hand side.







