Celtic moved six points clear of their rivals after beating Rangers at Ibrox, and are now in a good position to win the title.
The leaders took the lead after a free kick from Carter-Vickers, who scored the only goal of the game.
Rangers could not find a leveller in the second-half after broken glass was thrown on the pitch.
Giovanni van Bronckhorst's side tried to fight their way back as they faced a potentially knockout blow in their title defence but were met with stiff resistance as Celtic held on for a vital victory.
Substitute Liel Abada passed up two chances to seal it for the visitors, with Allan McGregor stopping the second attempt.
With a six-point lead and a 16-goal advantage with six games to play, the Socceroos are in a commanding position to win the league.
It is the first domestic home defeat for Rangers in more than two years, and was secured in the second half when Carter-Vickers and Carl Starfelt were outstanding in heading clear repeated crosses into their box.
Kemar Roofe started up front for Rangers but he missed both of his chances from inside the box.
Both sides had penalty claims waved away in a match of relentless running, with players also struggling with cramp in the closing stages.
Celtic extended their domestic run to 31 games with the vital three points.
The intensity and aggressiveness of Celtic's play has been praised this season, and it was evident in their derby win at Celtic Park.
The fact that they have the best defensive record in the league is less heralded, and this victory was ground out in the second half through a relentless work rate, good defensive positioning, and commitment to protect in their own box.
After a poor start from the visitors, Tom Rogic was the player who showed the most composure, and his movement and passing ability caused Rangers problems.
There should be some praise for the captain, who set up the first goal from nothing, and for Daizen Maeda, who ran constantly from the front.
No side has shipped a six-point lead at this stage of the season this century.
Rangers lack of attack in recent months was obvious. The home side reverted to the tactic of defending crosses rather than looking for space inside because Celtic seemed content to give up the wings.
It was even more surprising that they created the opening goal by pulling Josip Juranovic wide and freeing up Ryan Kent to run inside and cross for Ramsey to score.
They have a Scottish Cup semi-final against Celtic to look forward to, but the league now looks a long shot even if they keep fighting to the end.
A lack of a clear attacking identity continues to hamper Rangers domestically, despite the fact that Van Bronckhorst has got performances from the team in Europe. It feels like a long time ago.
After their trip to Braga in the last eight of the Europa League on Thursday, Rangers will have to travel to Paisley to face St Mirren next Sunday.
Celtic will have no European football on Saturday to distract them from their title quest.
Formation 4-3-3.88Juranovic20Carter-Vickers4Starfelt3Taylor18Rogic42McGregor41Hatate17Neves Filipe7Giakoumakis38Maeda
The match ended with Rangers defeating Celtic.
Rangers won the second half by a score of 1 to 2.
It was an attempt, Rangers. Leon Balogun tried a through ball, but Kemar Roofe caught it.
Calvin Bassey (Rangers) had a foul.
Liel Abada won a free kick.
An attempt was missed. Kemar Roofe's headed shot from the centre of the box misses to the left. Calvin Bassey had a cross.
Calvin Bassey won a free kick.
Foul by David Turnbull.
The attempt was saved. The left-footed shot from the left side of the box by Joe Ayodele-Aribo was saved in the bottom left corner. James Tavernier assisted.
Anthony Ralston was shown a yellow card for a bad foul.
Ryan Kent won a free kick.
Foul by Anthony Ralston.
An attempt was missed. The centre of the box is close, but the ball misses the right side. James Tavernier assisted with a cross.
Corner, Rangers. Carl Starfelt Conceded.
An attempt was missed. Kemar Roofe's shot from the centre of the box is wide to the right. A cross was assisted byConnor Goldson.
The attempt was blocked. Ryan Kent's shot from the right side of the box is blocked. Fashion Sakala assisted.
There is a yellow card for a bad foul shown to Nir Bitton.
John Lundstram won a free kick.
Foul by Nir Bitton.
Corner, Celtic. They had a match with Allan McGregor.