When United tied the score three minutes from time on Dylan Levitt's cross, it appeared as though they may earn themselves a point. Tony Watt may have been touched just a little bit after trying to flick a header.
But before Abada ensured Celtic went seven points ahead before Rangers visited St. Johnstone on Sunday, Furuhashi headed in from a last-second corner.
After Steven Fletcher's VAR-assisted penalty and Sead Haksabanovic's first two goals for Celtic in the first half, the hosts nearly paid the price for failing to make early second-half pressure pay off as United improved in the closing 20 minutes.
However, Ange Postecoglou's team once more managed to squeeze out three points, leaving United to suffer a totally different but nonetheless devastating loss to a team who had defeated them 9-0 in August.
When Haksabanovic scored the game's first goal in the sixth minute, it appeared that another beating would be in the cards. Before setting up the Montenegrin player for a tap-in after the Portuguese winger had been sent in by Reo Hatate, Jota had already missed two half-chances.
The tide swung the opposite way after a United corner, far from the floodgates being opened.
A visitor player got a flick-on as Alexandro Bernabei rose to head clear, but Fletcher's header smacked off the Celtic left back's arm behind his body as he was already in the air.
Although the Argentinian initially continued to play, referee David Dickinson pointed to the area and flashed a yellow card after turning to his monitor. Fletcher made a change.
The United goalkeeper Mark Birighitti made a great save on a header by Giorgos Giakoumakis, but it took Celtic some time to get back into the game. There was also a significant delay when VAR Nick Walsh looked for a possible red card after Craig Sibbald trapped the Greek striker with a high boot.
Dickinson wasn't even summoned to his screen after blowing for a foul.
Prior to Celtic regaining the lead after applying pressure after a corner in the 34th minute, Anthony Ralston was denied by Birighitti. The last recipient of Matt O'Riley's cross was Haksabanovic, whose first-time attempt was deflected in off the post by the United goalkeeper's feeble stop.
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In the first moments of the second half, Celtic had a clear advantage. When David Turnbull's header appeared to be heading into the goal after brilliant wing play from Jota, Aziz Behich came back to stop the ball on the line. That was the closest they came to scoring.
O'Riley and Giakoumakis both threatened on multiple occasions, while Turnbull nearly scored with a left-footed long-range shot, forcing two saves from Birighitti.
But as United excelled in dominance, Celtic lost some of their pace, and home supporters started to become nervous.
Furuhashi nearly scored with a glanced header, but Celtic quickly had two let-offs as time wound down to the final ten minutes.
Levitt's swiftly executed free kick, which sent Glenn Middleton through the right channel, caught the Hoops off guard. Joe Hart was beaten by the replacement, but Greg Taylor returned to clear off the line.
When Archie Meekison took the ensuing corner, Ryan Edwards rose to meet it with a clean header, but the ball deflected off the post.
Following a pass from fellow substitute Taylor, Celtic intensified their efforts to take a more substantial lead, and James Forrest headed against the underside of the crossbar.
When United tied the score through Levitt, Celtic was immediately surprised, but they reacted forcefully. Moritz Jenz was stopped by Birighitti following a strong effort, but Furuhashi quickly beat him with a header after Ralston flicked on an O'Riley corner.
Following a VAR check for offside, Abada quickly sprinted down the right wing before chipping Birighitti, and his goal was recognized.
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