A lovely goal from Adam Matthews, his first for the club, took them through a William Hill Scottish Cup fourth round replay but they made a meal of winning the tie. There were spells in the second half when they fell out of the game, even times when they were hanging on. Celtic have their place in the fifth round against Raith Rovers but the plaudits went to the part-timers from Arbroath.
Before the match John Christison, the Arbroath chairman, said his club had received a message of good luck from Jimmy Tarbuck, the comedian who had formed an affection for the town having performed there about a million years ago. Celtic knew they would be the butt of the joke if the Irn-Bru Second Division side pulled off an unthinkable result. It never came to that, but they were given a fright.
Celtic scored early but the longer the game wore on, the more the hosts grew into it and their fine striker, Steven Doris, was unlucky not to have a 65th-minute equaliser after Alex Keddie was penalised for a goalmouth challenge on Fraser Forster.
"It was a real test of their character and they have come through it very well," said Neil Lennon, the Celtic manager. "The longer the game went on, the more difficult the pitch became. It was almost like an ice rink. You could see a lot of passes going away from people because of that. So it became a real leveller. It became a difficult night for us.
"Coming here will be an eye-opener for some of the players. Everyone was here, including the cameras, to see if there was an upset. There was one [on Tuesday night] with Arsenal in England so I'm delighted that didn't happen to us. Arbroath made a real fight of it and they deserve enormous credit. We are in all the competitions and I can't ask any more than that."
Here was the night to answer the big question: sure, Celtic could beat Barcelona in the Champions League but could their players do it on a December Wednesday night in Arbroath? It was a test of their attitude and professionalism as much as anything else. If any of their side resented making the trip to the north east then they had no-one to blame but themselves. With all respect to Arbroath, who produced that admirable 1-1 draw at Parkhead, this was a fixture in Celtic's diary which should never have existed.
It may seem as though the temperature has never climbed above zero in Arbroath, yet in fact the cold was tolerable. Below zero, yes, but not eye-wateringly so. Celtic were spared Gayfield at its worst. There was no wind, rain, sleet or snow to trouble them and the pitch was okay at kick-off, although it became icy as the game evolved.
Having emerged with such great credit from Parkhead, Arbroath again performed admirably here. Their passing and movement troubled Celtic in the second half and they had their share of possession and corners. Paul Sheerin, the side's player-manager, might even have scored had his powerful shot not been blocked by Kelvin Wilson.
As is often the way, though, no sooner had that move ended than the favourites raced upfield and scored. Celtic had the early lead which should have been a platform for them when Matthews – playing at right wing-back in Lennon's 3-5-2 formation – sped up the wing and exchanged passes with Georgios Samaras. His finish was sublime, lashing the ball across goal and inside the far post.
Celtic would have had it won by half-time if Lassad hadn't made a mess of a terrific chance after Samaras's cushioned pass put Charlie Mulgrew's long ball on a plate for him. Earlier Samaras had planted a close-range header straight at goalkeeper Scott Morrison and Lassad later had the ball in the net but the effort was disallowed for offside.
This was nowhere near as comfortable as Celtic wished, though. Arbroath could not be easily put away. They competed well in midfield, worked tirelessly and always tried to play an attractive passing game when they broke forward.
Paul Currie burrowed into the Celtic box and rifled a drive over the bar early in the second half, and a Sheerin cross also caused a fright before Stuart Malcolm, Arbroath's mountainous centre-half, was booked for going in too hard on Forster.
Arbroath enjoyed their night – their fans taunted Celtic with "are you Montrose in disguise?" – although there was anger when they thought they had a valid goal only for it to be disallowed. Doris hooked the ball into the net after another cross had upset the Celtic defence but the referee saw a foul on Forster: Lennon agreed and Sheerin didn't.
Forster was involved again when Arbroath opened them up, the Celtic goalkeeper getting a crucial hand to substitute Connor Birse's one-on-one finish.
Lennon's frustration showed itself when he briefly answered back to a fan who had shouted an insult to him from the stand. Only the final whistle gave Celtic relief.
Scorer. Matthews (18)