Rangers will face Celtic in 8 December final
Helander converts Morelos cross before break
Morelos adds close-range brace after interval
First win in six semi-finals for Ibrox side
Rangers 2-0 Heart of Midlothian
Hearts are forced another - and their final - change as Michael Smith goes off injured.
Former Rangers forward Steven Naismith is thrown on, which obviously will mean a change in formation.
Rangers 2-0 Heart of Midlothian
Hearts haven't threatened but suddenly have two chances within a matter of seconds.
Uche Ikpeazu's header is cleared from in front of goal by Ryan Jack and, from the corner, Craig Wighton should do better than head wide from 10 yards.
Rangers 2-0 Heart of Midlothian
Neil McCann
Former Hearts & Rangers winger on BBC Sportsound
Quote MessageIt's that wide area again. This time Rangers do exploit it with a two-on-one against Aaron Hickey. It probably should be cut out, Aidy White is looking for a cut back instead of getting in line with Alfredo Morelos. You just can't see Hearts getting back into it now
Alfredo Morelos
Whatever Austin MacPhee said at half-time, it is undone within seconds of the second half as his side fall further behind.
Hearts are all over the place as a cross comes into the penalty box and James Tavernier plays it low into the six-yard box, where Alfredo Morelos hammers it home for his 19th goal of the season.
Rangers 1-0 Heart of Midlothian
Hearts get the second half under way. Penny for Austin MacPhee's thoughts...
HT: Rangers 1-0 Heart of Midlothian
Here come the players out of the tunnel.
Will Rangers build on their lead and secure a final against city rivals Celtic or will Hearts stage an unlikely comeback?
HT: Rangers 1-0 Heart of Midlothian
Neil McCann
Former Hearts & Rangers winger on BBC Sportsound
Quote MessageGetting goals from wide areas, full-backs coming into the penalty box, midfielders, centre-backs coming up, it means the opposition has to spread their focus instead of zoning in on one threat. We've seen it from Celtic through the years, goals from all over the place. It's a fantastic quality to have in a side.
HT: Rangers 1-0 Heart of Midlothian
Neil McCann
Former Hearts & Rangers winger on BBC Sportsound
Quote MessageThe maroon jerseys are static for the goal - it's pretty poor. They've defended okay so far, but that was such a cheap goal in such a late stage of the first-half. You could have been heading in there at 0-0 with Rangers the ones being frustrated
Image source, SNSFilip Helander scored just on the stroke of half-time
It might be a bit early to vote yet - it can all change in the next 45 minutes - but our player rater is now up and running.
Which Rangers player did you rate man of the match as the Ibrox club beat Hearts at Hampden to set up a Scottish League Cup final against Celtic?
Read MoreHT: Rangers 1-0 Heart of Midlothian
Neil McCann
Former Hearts & Rangers winger on BBC Sportsound
Quote MessageAustin MacPhee's gameplan has been blown to smithereens with Glenn Whelan going off injured, going with him his leadership qualities. Steven MacLean looks as if he's lost his composure and it's maybe because of the lack of support he was getting
HT: Rangers 1-0 Heart of Midlothian
Billy Dodds
Former Scotland striker on Sportsound
Quote MessageThe first half has been dominated by Rangers. Hearts have been trying to take some possession, playing narrow, leaving a lot of wide space. That last minute goal from Helander is a blow for Hearts and it will be hard to come back from that, but you cannot say Rangers don't deserve it
HT: Rangers 1-0 Heart of Midlothian
The statistics tell the story of the first 45 minutes - Rangers have dominated and Filip Helander's goal was one of four shots on target.
Image source, SNSHT: Rangers 1-0 Heart of Midlothian
Neil McCann
Former Hearts & Rangers winger on BBC Sportsound
Quote MessageThere's the difference - you normally see this with strikers gambling, attacking a ball put across with pace. You wouldn't normally expect it from a defender, or Filip Helander, but that's what's happened. The Hearts defenders are just static. That's turned the game on its head
Hearts caretaker Austin McPhee would have been preparing one kind of half-time team talk. Now he has to deliver another.
It looked like his side were going to survive until the break despite Rangers dominating possession.
However, Filip Helander made them pay for some poor marking at a corner with his second goal since signing from Bologna - the defender's second in three games.
It's a long way back for a Hearts side who haven't won in five games, are working under a caretaker manager and have only been in the opposition penalty box once.
Filip Helander
Just when Hearts looked like surviving until the break, Filip Helander of all people steps up to open the scoring.
Alfredo Morelos rolls the ball into the penalty box as Hearts half clear a corner and the Swedish defender is there unmarked to tap home from 10 yards.
Uche Ikpeazu, just on as a sub, was caught sleeping as he was supposed to be marking the scorer.
Rangers 0-0 Heart of Midlothian
Michael Smith is the latest Hearts player to be hobbling as he concedes a corner.
Steven Davis fires a volley that deflects wide and Hearts have two minutes of stoppage time to survive.
Rangers 0-0 Heart of Midlothian
Neil McCann
Former Hearts & Rangers winger on BBC Sportsound
Quote MessageBrilliant feet from Ryan Kent. Just a flash of how dangerous he can be
Rangers 0-0 Heart of Midlothian
Ryan Kent is starting to show the kind of form he enjoyed before his recent injury.
The former Liverpool winger fires a dipping drive from all of 20 yards that strikes the outside of a post.
Rangers 0-0 Heart of Midlothian
Neil McCann
Former Hearts & Rangers winger on BBC Sportsound
Quote MessageI think we're all of the opinion Uche Ikpeazu should have started the game, but you can't take a risk - Steven MacLean is fortunate there. Saying that, there wasn't much in it, though. I think you're entitled to stick a boot out
Rangers 0-0 Heart of Midlothian
Austin MacPhee makes that change.
Uche Ikpeazu did not look pleased at being on the bench, but he gets his chance earlier than expected as Steven MacLean is hauled off before he is sent off.
But that means Hearts only have one substitution left after Glenn Whelan went off injured.