Two sublime strikes from Paulo Bernardo and Kyogo Furuhashi made the difference against the visitors, who were made to pay for several missed opportunities in the first half and had their misery compounded when Leon Balogun received a straight red card.
A sensational James Tavernier free kick in the dying embers made the closing stages far nervier than it should have been for the holders, but as the clock ticked over to three figures, the Bhoys would end 2023 on the highest of highs.
The teams were greeted by a full Celtic contingent in Parkhead due to the ongoing dispute surrounding away tickets, meaning not a single Rangers fan would witness the action from the stands, and Jack Butland was unsurprisingly tested early doors.
The Englishman was forced to tip a Furuhashi effort behind with just five minutes gone, although Joe Hart had to be alert to eliminate the danger from a low Ross McCausland cross two moments later.
The engrossing end-to-end action continued in the 12th minute, as Bernardo met a Luis Palma cross but flashed his header wide of the far post, before the Portuguese sent another fierce strike into the side netting in the 23rd minute.
However, just two minutes after that squandered opening, Bernardo displayed exceptional technique to propel Celtic into the lead, meeting a Palma corner with an exquisite half-volley into the side of the net.
The bedlam that followed saw one of the advertising hoardings collapse and Bernardo receive a yellow card for his role in the trouble, but as the half drew to a close, Rangers slowly but surely turned the screw.
Cyriel Dessers wasted a golden chance in the 33rd minute, finding himself one-one with Hart but delaying his shot for far too long, allowing Alistair Johnston to put a foot in and smother the ball back to his goalkeeper.
An injury to Stephen Welsh - whose spot was filled by Maik Nawrocki - provided Rangers with another fillip, as Todd Cantwell and McCausland both made Hart work in the 38th and 42nd minutes respectively.
Brendan Rodgers's men nevertheless made it to half time with their slender lead intact, thanks also in no small part to a Johnston handball in the box which went unpunished due to an offside against Abdallah Sima, and within just 75 seconds of the restart, Parkhead erupted into euphoria once again.
Renowned for his penchant for goals this season, Matt O'Riley turned provider with a stunning pass inside to Furuhashi, who shifted the ball onto his left foot inside the D and left Butland with no chance with a wonderful strike into the top corner, his fifth goal in his last four Old Firm starts.
Furuhashi's thunderbolt sucked the life out of Rangers, who had little in the way of an immediate response to the hosts' second until Dessers rifled a shot into the side netting from a tight angle in the 61st minute.
Any wafer-thin hopes of a Gers fightback were virtually extinguished in the 71st minute thanks to a one-man disasterclass from Balogun, whose misplaced touch fell at the feet of Furuhashi, and the 35-year-old was forced to commit a last-man foul on Daizen Maeda as the Celtic striker raced through on goal.
Referee Nick Walsh had no choice but to dismiss Balogun, but Clement's side still forced a nail-biting finish in the 88th minute, as captain Tavernier beat Hart all ends up with an astonishing free kick from the left, which sailed into the top corner of the net.
Groans were audible as eight minutes of added time went up on the board, and Rangers were still huffing and puffing with over 100 minutes gone, but Celtic defended valiantly when it mattered most.
The champions' warranted success allowed them to open up an eight-point lead over Clement's men at the top of the Scottish Premiership table, although the Gers still possess two games in hand, leaving the fight for title glory very delicately poised indeed.
Celtic's opening match of 2024 sees Rodgers's men head to St Mirren on Tuesday, while Rangers also have two full days to recuperate before they host Kilmarnock.