Fellow Japanese attacker Daizen Maeda opened the scoring for the visitors in the fifth minute after taking advantage of atrocious Gers defending.
The Light Blues looked forlorn going down the tunnel at half-time but Ryan Kent curled in the equaliser two minutes after the break before skipper James Tavernier slammed in a penalty five minutes later.
However, in the 87th minute, Furuhashi flashed a shot from 12 yards high into the net to keep Ange Postecoglou’s side nine points clear of their Glasgow rivals at the top of the table.
Following a minute’s silence as tribute to the 1971 Ibrox Disaster – which was not perfectly observed – another frenetic and breathless Glasgow derby commenced.
Rangers boss Michael Beale was pleased that Alfredo Morelos had shrugged off a tight hamstring.
However, the Colombia striker was partly to blame for the visitors’ early opener.
His short pass in-field was intercepted by the darting Maeda who brushed off a poor attempt at a challenge by Tavernier and sped past Connor Goldson before slotting under keeper Allan McGregor from 14 yards.
Celtic, their players wearing black armbands following the deaths of former striker Frank McGarvey, Pele and Pope Benedict XVI, and with Canada right-back Alistair Johnston making his debut, looked in the mood.
Celtic skipper Callum McGregor had a drive from outside the box tipped around the post by his goalkeeping namesake but the corner came to nothing.
Josip Juranovic replaced the injured Hoops left-back Greg Taylor in the 21st minute and five minutes later Celtic almost gifted Rangers an equaliser.
Goalkeeper Joe Hart’s clearance was blocked by Morelos who played the ball to midfielder Glen Kamara who set up Kent for a drive.
The forward’s effort was tipped on to the post by the recovering Hart before Fashion Sakala’s shot was blocked for a corner by Carl Starfelt.
Celtic survived but Rangers took encouragement and a greater share of possession and pressure, although Morelos missed the target with two headers from corners.
Kent, however, was more accurate soon after the interval when he was set up by Sakala, turning inside Johnston and curling a shot from 16 yards across Hart and into the net.
Rangers fans soon had more to cheer.
When Starfelt took Sakala’s leg away in the box referee John Beaton pointed to the spot and Tavernier made amends for his earlier indiscretion by smashing the ball high past Hart.
The match had swung towards the Light Blues and on the hour mark Postecoglou replaced Forrest and Matt O’Riley with Liel Abada and Aaron Mooy, and Celtic responded.
Ibrox held its breath as Beaton checked for a possible handball in the Rangers penalty area after a Starfelt shot hit Goldson, but play continued as it did following a second possible penalty claim for Celtic when again the ball came off Goldson minutes later.
The game stretched in the increasingly tense final stages.
Rangers countered in the 84th minute but backtracking Celtic defender Cameron Carter-Vickers brilliantly blocked a goalbound shot from Malik Tillman.
But there was more drama to come and in the 87th minute, Celtic snatched an equaliser.
Substitutes Mooy, Jota and Georgios Giakoumakis were all involved in an attack inside the Gers box and when the ball fell to Furuhashi, the Japan striker lifted his shot high past McGregor for a share of the spoils as seven minutes of added time could not provide a winner.