The Light Blues fell behind inside 30 seconds to a Daizen Maeda goal, before Matt O’Riley doubled his side’s advantage from the penalty spot.
A James Tavernier spot-kick reduced the arrears, before the Gers levelled with three minutes remaining when Abdallah Sima’s deflected strike beat Joe Hart.
A late strike from Adam Idah then appeared to deliver all three points to the away side, but a sumptuous strike from Rabbi Matondo in stoppage time salvaged a point for Philippe Clement’s side in an exhilarating second half showing.
Not even 30 seconds had elapsed when Rangers fell behind in the contest, with James Tavernier’s attempted clearance cannoning off Daizen Maeda from 25 yards out and beating Jack Butland all ends up.
It was certainly a far from ideal start for Clement’s side, although they passed up the opportunity to level proceedings just after the 20th minute mark when Connor Goldson headed over from Mohamed Diomande’s pinpoint corner-kick delivery.
Rangers were indebted to Butland moments later, however, as Maeda was denied from close range as the Japanese looked to curl into the far corner. Moments later, Reo Hatate’s rasping effort from the edge of the penalty area whizzed wide of the Rangers goal.
There was another let-off for the home side on the half-hour mark when Nicolas Kuhn’s delivery was met flush on the head by Matt O’Riley who drew a fantastic diving acrobatic stop from Butland.
However, the visitors soon doubled their advantage moments later from the penalty spot. A delivery from the right-hand side in search of Celtic defender Liam Scales didn’t initially appear to involve anything untoward, but a closer look from VAR alerted referee John Beaton of a potential handball from Goldson.
A trip to the pitchside monitor confirmed the suspicions, with O’Riley grabbing the ball for Celtic and dispatching from 12 yards to leave the Gers with it all to do in Govan.
Opportunity beckoned for Fabio Silva on the stroke of the half-time interval to reduce the arrears after a smart turn from Scott Wright in midfield, although the Portuguese was thwarted by a sprawling save from Joe Hart on his unfavoured side.
Abdallah Sima was summoned from the substitutes bench for the start of the second period, with the Senegalese looking to test his pace on the right-hand side and haul Rangers back into the contest.
It was Celtic, however, who fashioned the first opportunity after the restart when the ball made its way to Hatate at the edge of the penalty area, but the Japanese midfielder drove his effort straight down the throat of Butland.
What followed was a manic five minutes as Ibrox came alive to back the team.
Indeed, the Gers were awarded a spot-kick after Silva was brought down inside the penalty area by Alistair Johnston following a neat chop away from the Canada international. Although referee John Beaton initially cautioned the Portuguese for simulation, he was advised by VAR to take a closer look, with footage clearly illustrating the forward was tripped by the Celtic full-back.
The captain stepped forward and was emphatic in arrowing his penalty into the top corner, halving the deficit and bringing Ibrox to its feet in support of Clement’s side.
And Rangers thought that the equaliser had arrived only moments later when Cyriel Dessers wheeled away in celebration following a swift counter-attack.
The home side sprung forward with pace in abundance as Dessers fired home from Sima’s cut-back after Celtic failed to clear their lines inside the penalty area, but the Ibrox celebrations were cut short after the referee took a trip to the pitchside monitor and adjudged that Tom Lawrence had fouled Tomoki Iwata in the build-up.
It would prove to be Lawrence’s final involvement of the contest as he was replaced by Todd Cantwell, with Rabbi Matondo also introduced in place of Silva.
Rangers continued to advance forward in search of a priceless leveller, going close when Matondo jinked inside and had goalbound effort blocked en route by Cameron Carter-Vickers.
The leveller then arrived for Rangers with minutes remaining when Sima’s strike took a wicked deflection off Liam Scales and wrongfooted Hart.
Amid the celebrations, however, Celtic advanced down the opposite end and appeared to win the game when Adam Idah wriggled free inside the penalty area and shot under Butland.
Rangers, though, showed immense fight until the full-time whistle, snatching a draw from the jaws of defeat when Matondo jinked menacingly inside and curled an unstoppable effort into the far corner.
RANGERS: Butland, Tavernier, Goldson (Balogun, 90), Souttar, Sterling, Lundstram, Diomande (Dowell, 76), Lawrence (Cantwell, 68), Wright (Sima, 45), Silva (Matondo, 68), Dessers
Subs not used: McCrorie, Barisic, King, McCausland
CELTIC: Hart, Johnston, Carter-Vickers, Scales, Taylor, Iwata, Hatate (McGregor, 64), O’Riley (Bernardo, 81), Kuhn (Yang, 64), Maeda, Kyogo (Idah, 68)
Subs not used: Bain, Nawrocki, Forrest, Ralston, Welsh