Now they are eight adrift and needing a run of several wins to reignite their hopes of a 54th title in Walter Smith’s final season at the club.
Gary Hooper’s first-half double put the hosts ahead and Kris Commons capped a miserable day for the Ibrox team with a third after the break.
Gers, of course, will seek revenge when they return to the city’s east end next midweek for a Scottish Cup replay.
In the meantime, their remit is to pick themselves up for their return Europa League game in Lisbon and next Sunday’s home contest with St Johnstone.
Smith made three changes to the side drew 1-1 with Sporting on Thursday and none of them were terribly surprising.
Nikica Jelavic returned to the team after being ineligible for that game and he led the line as a lone striker.
He was supported by Steven Naismith – also back in the side after a midweek omission – while Kyle Bartley made his first Old Firm start after impressing against Motherwell.
The on-loan Arsenal youngster was the first man to make an impression on the game, receiving a yellow card just three minutes in for a foul on Scott Brown.
Thankfully for Gers, the resulting free kick from Commons from fully 40 yards was poor as it skimmed the grass and rebounded off the wall.
Home fans were intent for most of the early exchanges on booing El-Hadji Diouf but he set up the first chance after he won a corner then took it himself.
The Senegalese forward found Madjid Bougherra from the set piece, with his goalbound header cannoning off Georgios Samaras and away.
Another Diouf corner moments later almost gave Jelavic his first sight of goal but he couldn’t quite connect with the ball.
At the other end, Hooper showed great pace to burst away from Bartley then David Weir but a combination of the two defenders eventually denied him once they had regrouped.
After the frenetic start of the last game between these two, this match was a bit tamer initially.
But then, with almost 17 minutes gone, Celtic took the lead with their first attempt on goal and it was a poor goal for Rangers to lose.
Hooper was able to step beyond Weir with relative ease and he took a touch to steady himself before sliding the opener under Allan McGregor.
Gers hit back and Jelavic and Diouf linked up on the edge of the box but the Croatian fired over and was always going to struggle to hit the target as he was crowded out.
Jelavic then turned provider as he slipped Naismith through but he was forced out wide and his low ball into the box was just behind Steven Davis.
The visitors were enjoying their best spell of pressure so far and a deep Diouf ball in from the left caused all sorts of problems before it was scrambled clear.
But when Celtic next charged upfield they doubled their lead with just 27 minutes on the clock and it was Hooper again who struck.
Samaras brought the ball out of midfield and picked out Emilio Izaguirre, who broke the offside trap then squared for the home striker to bundle in.
Celtic’s tails were up and it was up to Smith’s team to come up with a quick response but Jelavic’s shot was weak after good work by both him and Steven Whittaker.
Rangers’ play in midfield was actually decent enough on the whole in the first half but they let themselves down too often with a poor final ball.
Added to that, the fact Neil Lennon’s side was moving from back to front with pace meant the Ibrox outfit’s task was as big as anything they had faced all season.
Naismith struck his attempt from 25 yards after a Diouf corner was cleared well enough but it was always running wide.
And as the half-time whistle went, it was hard for away fans to argue their team deserved anything from the game at that stage.
Smith was forced into making an interval substitution, with Naismith’s suspect hamstring flaring up again and meaning he had to be replaced by Kyle Lafferty.
Within 60 seconds of the restart, Jelavic had a chance to pull one back with a glancing header but he nodded just wide from Davis’ centre.
Celtic then had a chance to add a third when McGregor only got one hand to a Samaras cross and Brown headed over him but Sasa Papac had got back to put the ball behind.
Play was opening up a little and Diouf had his first opportunity when he was found by Lafferty.
The African did everything right as he brought his pass down really well and he tried to lift over Fraser Forster but the keeper made a good save.
Rangers were starting to get more space and you sensed nerves were beginning to creep into the home ranks.
But when Diouf found Jelavic and he headed two yards wide again, that took the pressure off the Parkhead team and they were able to move upfield once more.
It took until the midway point of the second period for the away side to conjure another chance, with Jelavic hitting the target this time with a header but having it saved.
Just a minute later, Celtic made sure of the points as Commons made it 3-0 with a swerving finish.
The former Derby winger collected the ball on the edge of the area and after a touch on to his right foot, he drilled past McGregor.
Jelavic had another couple of opportunities to give the visitors a chink of light but this was a day in which he never found his range.
Now, however, more than ever, Gers need him and his team-mates to get back on track quickly as they look to salvage their dream of silverware in the weeks ahead.