Celtic dominated the first half and opened the scoring after just 21 seconds in freakish fashion, as an attempted clearance from Rangers captain James Tavernier cannoned off the chasing Daizen Maeda and flew into the bottom corner.
The Hoops were then awarded a penalty following a VAR check after the ball crashed against the elbow of Connor Goldson while Rangers were defending a corner. Matt O'Riley stepped up a coolly dinked his effort from 12 yards straight down the middle to double the visitors' advantage.
Celtic were deservedly in front and should have been out of sight in the first half, but Rangers valiantly fought back and halved the deficit when Tavernier converted a controversially-awarded penalty after Fabio Silva - who was initially booked for diving - was deemed to have been fouled by Alistair Johnston following a VAR review.
Rangers then restored parity five minutes from time when Abdallah Sima's deflected volley flew into the top-right corner, but Celtic regained the lead just 71 seconds later courtesy of a low-drilled shot from Adam Idah under the body of an unsighted Jack Butland.
It was the hosts who had the last laugh, though, as Rabbi Matondo netted a stunning 93rd-minute equaliser, almost a carbon copy of his strike against Hibernian last weekend, as he cut inside from the left and curled a sweet right-footed strike into the far corner to salvage a point for the Gers.
Celtic have now won only one of their last five visits to Ibrox and have dropped points in two of their last four Scottish Premiership matches.
The Hoops remain at the top of the table heading into their final six matches of the season, but Rangers only sit one point behind their Glaswegian rivals and crucially have a game in hand.
Philippe Clement: 'Rangers are the moral winners'
Clement has commended the fighting spirit of his Rangers side to come from behind and salvage a point, and has encouraged his players to adopt the same mentality heading into the final few weeks of the season.
"In the first moment, I am proud with what the guys showed. I don't have a good word for our start that I can use on television. It's the worst scenario you can have to go behind in the first minute," Clement told Sky Sports.
"To get a penalty against us like that is also something bad, every manager in the world gets stressed out by this handball rule. The ball deflects at the last moment, my defender jumps with his arm because that's how you jump.
"In the second half, the boys showed their real personality. There are so many steps that have been made in the last couple of months. This is a really clear signal to the outside world about what this dressing room is about, that they have a winning mentality, and I'm really proud of that.
"There are moments I can say what I said at half time - it's better I don't say what I said today. I'm happy about the reaction, they showed personality and at the end. We are the moral winners of this fight, of this game.
"With a lot of passion, everything these supporters want, everything this club wants. Everything this club is about, they showed in the second half. They need to show it in the next couple of weeks too in every challenge we have.
"There's a big evolution in that. They showed something special today. I always believed they had the quality to do it, and they showed it in the second half. It doesn't give guarantees, but if you keep pushing like we did in the second half, you can turn things even against a good team like Celtic."
Brendan Rodgers: 'Title race still in our hands'
Rodgers, meanwhile, was critical of the decision to award Rangers a second-half penalty, but the Celtic manager has taken positives from his side's performance at Ibrox and claims the title race is still in their hands.
"It was a fantastic game, full of lots of events," said Rodgers. "I'm so proud of the players, we were so much the better team, leading through to the penalty, our composure on the ball, our pressing, everything.
"We restricted Rangers to virtually nothing and looked a real threat in the first half, 2-0 up and could have had one or two more if we picked the right pass.
"The penalty changed the momentum, I thought it was a good decision on the pitch (to initially book Silva for diving) and watching it back on the replays it's good recovery defending from Johnston. He gets a nick on the ball, and the player has gone down looking to simulate the penalty.
"That gave them a little lift in the game, then we're unlucky with the deflection for 2-2. Then you're looking at the response, and being here with no support to help us, the players got themselves back in front brilliantly - It's a great finish from Adam, and it looked like we'd go on to win it. Then Matondo scores a very, very good goal.
"But to come here, play with that courage and mentality, have the heart and fight to get a result, to come away with it still in our hands, I'm very, very pleased."
Celtic are back in action next Saturday at home to St Mirren, but Rangers could climb to the summit before that fixture if they beat Dundee at Dens Park on Wednesday night.