Kemar Roofe made the winning penalty.
The penalty by Kemar Roofe with five minutes left gave Rangers an important victory against Hibernian.
Ryan Kent drew a foul from Ryan Porteous and Roofe was able to convert to give the champion a dramatic win.
It was a laboured first hour as Hibs looked good for at least a draw, but it was Morelos who missed the best chance.
The win moves Rangers seven points clear of Celtic and puts the pressure on their Glasgow rivals, who face Hearts on Thursday.
Hibs have lost six of their last seven league matches.
Reaction as it happened.
The League Cup semi-final was played 10 days before Giovanni van Bronckhorst took over as Rangers manager.
They kept a clean sheet for the first time in eight league matches, as they learned a lot from that game.
However, the leaders failed to sparkle going forward with Hibs goalkeeper Matt Macey only forced to make a few routine saves, although an excellent one to tip Ianis Hagi's low shot past a post.
He didn't have to stop Morelos' first-half goal as he headed wide despite moving brilliantly between the Hibs' centre-backs to get on the end of Joe Aribo's clever cross.
Hibs pressed Rangers in the middle and stifled their build-up play, but lacked a killer instinct in the final third.
Chris Cadden's low shot was the best chance the home side had to test Allan McGregor.
As time wore on and legs tired, the game became stretched and Kent showed his strength.
The Englishman stood up Porteous and cut inside, forcing the Hibs defender to leave a leg in and give the referee a decision to make. Kent went down easily, but there was contact.
Roofe, who came on for Morelos in the second half, calmly sent Macey the wrong way.
Josh Campbell was the man of the match.
Campbell was excellent for Hibs, working relentlessly off the ball after signing a new deal. Rangers defender Connor Goldson made some strong interventions in his own box.
What did we learn?
The short-term approach seems to be pragmatism.
James Tavernier and Borna Barisic were asked to retreat to try and plug the defence. Three weeks ago, they were humiliated by a man who ran into the channels.
They looked more threatening when they went direct and on the break, though they struggled to play past Hibs' press on the deck.
The new manager may want to get the ball forward quicker. Aribo looks like he's enjoying more freedom.
Things broke down in the final third of the game. Campbell and Joe Newell were in the middle. Rangers were stopped from coming through the middle by their man-for-man approach.
Porteous gave up the crucial penalty. Kent went down easily, but the Hibs defender should have kept his leg out.
Hibs need wins quickly and must take advantage of a busy run of games this month.
What they said.
The penalty is something Jack Ross would want in the opposition box. That doesn't mean it's a penalty. I had no idea at the time, but I watched it again and saw that Ryan pulled his foot away. There is very little contact.
We would argue the case for it not to be given if they were given. I don't think we deserved that or Ryan deserved that.
Rangers manager Giovanni van Bronckhorst was on Sky Sports. It was a tough game. It was very close and both sides played very physical.
We'll take the win and three more points.
What's next?
There are two home league games on Saturday, one for Motherwell and the other for Rangers at Ibrox.
Hibernian
The Rangers are a team.
Line-ups.
Match statistics.
Live text.
Formation 3-4-1-2.
27Cadden22Doyle-Hayes11Newell3Doig
1Macey
6McGinn was booked for 90 minutes.
5eous.
4Hanlon.
Substituted forMurphy at 86' minutes.
The book was written at 29 minutes.
11Newell
3Doig
Substituted for Allanat.
10 Boyle.
15Nisbet.
Substitutes.
8Wright.
13Gogic
Stevenson is a person.
18Murphy
21Dabrowski
Allan
25Scott.
Formation 4-2-3-1.
2Tavernier6Goldson3Bassey31Barisic
McGregor is a person.
2Tavernier
The book was written at 24 minutes.
3Bassey.
31Barisic
Substituted forArfield 66' minutes.
18Kamara.
17Aribo
7Hagi.
Substituted forLundstramat 86' minutes.
Substituted forRoofeat 66' minutes.
Substitutes.
4Lundstram
16Patterson
23Wright.
25Roofe
30Sakala
McLaughlin is 33
37Arfield
The match ended with Rangers winning 1.
The second half ended with Rangers winning.
Ianis Hagi of the Rangers had a foul.
The defensive half is where Joe Newell won the free kick.
James Tavernier of the Rangers.
Jamie Murphy won a free kick.
The yellow card shows Paul McGinn.
An attempt was missed. Ryan Porteous's head is high and wide to the left. The cross was following a corner.
Corner, Hibernian. The man was Conceded by Glen Kamara.
Kemar Roofe of the Rangers had a foul.
The free kick was won by Paul McGinn.
The attacking half has a free kick.
Foul by Martin.
Ianis Hagi won a free kick.
Foul by Paul Hanlon.
The substitution was for Hibs. Josh Campbell was replaced by Scott Allan.
The substitution was for Hibs. Chris Cadden was replaced by Jamie Murphy.
The Rangers had a substitution. Ryan Kent was replaced by John Lundstram.
Goal! Rangers 1, Hibernian 0. Kemar Roofe converted the penalty with a right footed shot to the centre of the goal.
The Rangers were given a penalty. Ryan Kent is in the penalty area.
