The key moment of the first half came when Rangers midfielder Lee Wallace's early header may have crossed the line before Hoops keeper Fraser Forster clawed it back.
However, after Ledley buried his header from a Charlie Mulgrew corner into the back of the net seven minutes after the break, the home side stamped their superiority on the game and ran out deserved winners.
It was Celtic's ninth SPL win in a row and confirmed the turnaround in fortunes since November 5, when they were 15 points behind the champions, albeit with two games in hand.
Neil Lennon's men look to have the bit between their teeth while struggling Rangers have it all to do to recapture their form and on the evidence of tonight, that is likely to need fresh faces when the January transfer window opens.
Lennon made two changes to his in-form side, both something of a surprise.
Right-back Adam Matthews replaced Cha Du-ri while defender Thomas Rogne came in for Ki Sung-yueng and swapped places with Victor Wanyama who moved into midfield.
Rangers boss Ally McCoist made three changes, one enforced after defender Dorin Goian was sent off against St Mirren at the weekend.
Kyle Bartley took Goian's spot while Kirk Broadfoot came in for the injured Steven Whittaker and wideman Sone Aluko, instead of Maurice Edu, replaced Gregg Wylde, a decision believed to have been made after arrival at the ground.
Midfielder Lee McCulloch remained in the side after the Govan club appealed the red card picked up at St Mirren Park.
Celtic skipper Scott Brown tried to intimidate Wallace as they lined up for kick-off, staring intensely at the Rangers midfielder.
However, in the seventh minute Wallace's header at the back post from an Aluko cross looked like it may have crossed the line before Forster forced it back onto the post.
As the driving wind gave way, but only a little, to torrential rain, Celtic took the initiative.
Brown had a drive from 14 yards saved by Allan McGregor before Hoops striker Georgios Samaras had the ball in the Light Blues' net only to be ruled offside.
The conditions continued to dominate the game but in the 24th minute, after Aluko's corner from the left had been headed goalwards by striker Nikica Jelavic, Rangers defender Carlos Bocanegra inadvertently helped the ball over the bar from two yards.
However, the Hoops had the best of the possession and in the 35th minute striker Gary Hooper took a Samaras knock-down, turned and forced McGregor into another save before James Forrest blazed an angled drive over the bar following a corner.
Both sides went at each other from the start of the second half but it was Celtic who struck after McGregor had tipped a great drive from Forrest over the bar for a corner.
From Mulgrew's delivery from the right, Ledley rose high in a packed penalty area to direct his header past the Rangers keeper.
The complexion of the game changed immediately.
Rangers were on the ropes, trying desperately to stem the green and white tide and the Ibrox side were lucky to escape when Hooper appeared to be wrongly flagged offside as he raced clear of the visiting defence.
Aluko was replaced by Wylde after 66 minutes as McCoist tried to inspire a response from his side which came in the form of a couple of spectacular efforts from Jelavic, one of which flew over the bar and the other into the arms of Forster.
In the 76th minute Celtic midfielder Beram Kayal went off injured on a stretcher, to be replaced by Ki, after a clash with McCulloch which originally looked to have hurt the Ibrox player more.
Moments later, McCulloch and Wallace went off to be replaced by Edu and David Healy, who was soon booked for a scything touchline tackle on Forrest.
As the game entered the final stages, and Celtic had not sealed the win, the tension increased and the visitors looked in danger of losing the plot.
With four minutes remaining Rangers striker Kyle Lafferty was booked for a late challenge on Matthews before Anthony Stokes replaced Hooper.
There were five added minutes but Rangers, desperate as they were, failed to threaten Forster leaving Celtic deserved winners and league leaders going into 2012.