At stumps, he was unbeaten on a glacial 44 off 120 balls and Travis Head was not out on nine after nearly three hours' play were lost to rain.
Pakistan's bowlers found plenty of movement in the overcast conditions and were rewarded with the wickets of David Warner (38), Usman Khawaja (42) and Steve Smith (26).
But a patient Labuschagne was immovable as the hosts look to seal the three-Test series after thumping the visitors by 360 runs in Perth.
"It was a good day as a bowling unit, a bit unlucky that we haven't got more wickets," said Pakistan paceman Hasan Ali, who removed Khawaja.
"I think we are a bit ahead of them and looking forward to tomorrow."
Pakistan captain Shan Masood won the toss and opted to bowl first on a pitch suited to the seamers.
Spearheaded by Shaheen Shah Afridi, they bowled a good length and found early swing.
"(We are) okay. Another wicket less would have been great, but credit to the way Pakistan bowled. They bowled unbelievable channels," said Warner.
"But I think going into tomorrow we're in a pretty good position. Anything with a four in front of it would be great, but it is going to be a tough grind."
Warner, who made 164 in the first innings at Perth in his farewell Test series, was dropped on two by Abdullah Shafique, who put down a regulation catch at second slip.
He was also fortunate to get away with an edge that sailed over the slips for a boundary on 17.
His luck ran out with a rash shot off part-time spinner Agha Salman in the final over before lunch, with Babar Azam holding a catch at slip off a thick outside edge.
Survival mode
Warner's long-time opening partner Khawaja has been embroiled in a dispute with the International Cricket Council over how he can bring attention to the humanitarian crisis in Gaza.
He was denied a bid to display a sticker showing a black dove holding an olive branch on his bat and instead played with the names of his daughters on his shoes.
The 37-year-old hit a boundary off the second ball he faced and looked destined for a big score before speedster Hasan Ali, back in the team after being overlooked for Perth, drew an edge that Salman took well in the slips to leave Australia on 108-2.
With dark clouds overhead, the lights were turned on mid-afternoon with Labuschagne and Smith in survival mode as the bowlers turned the screws before the rain arrived.
The conditions eventually cleared and play resumed in front of a sparse crowd, with many of the 62,000 fans giving up and going home.
Smith and Labuschagne continued to play defensively, with runs hard to come by.
Labuschagne finally relieved some pressure when Aamer Jamal was brought on, hitting his first boundary in 75 balls, with the grin on his face telling a story.
It was similarly slow going for Smith, who was given out lbw on 19 after a big shout from Afridi, but a review showed the ball going high.
He was less fortunate against Jamal soon after. The umpire ignored an appeal from wicketkeeper Mohammad Rizwan for a catch, but Pakistan reviewed and it showed a faint edge, ending a 147-ball partnership.
