Labuschagne top-scored with 80 in Australia's second-innings 246 on the third day of the third Test.
It was his third successive fifty since being drafted in as world cricket's inaugural concussion substitute in place of Australia star batsman Steve Smith during the second innings of the drawn second Test at Lord's.
England were left needing a mammoth 359 for victory in a match where a win for Australia would see then retain the Ashes at 2-0 up with two to play in a five-Test series.
Only three sides have made more than 300 to win in the fourth innings of a Test at Headingley -- Australia (404-3 in 1948), England (315-4 against Australia, 2001) and West Indies with 322-5 two years ago.
At lunch, England were 11-0.
The fact they survived four overs without losing a wicket was greeted by ironic cheers from a sun-drenched crowd following England's woeful 67 all in their first innings -- seven fewer than the 74 Labuschagne made himself.
Australia fast bowler Josh Hazlewood took five wickets on Friday as England were skittled out with their lowest Ashes total for 71 years.
But it was also the fourth time in 18 months that England had been dismissed for under 100 in a Test.
Australia resumed on 171-6, already 283 runs ahead, with Labuschagne 53 not out.
Labuschagne drove Stuart Broad for a textbook four through extra cover to go to 60 only to be dropped next ball when diving wicketkeeper Jonny Bairstow dropped a one-handed chance heading towards England captain Joe Root at first slip.
It was Labuschagne's third reprieve of the innings, with Root and Bairstow, on their Yorkshire home ground, having dropped him on 14 and 42 respectively on Friday, when he was also 'caught' off a Ben Stokes no-ball.
Archer did remove James Pattinson (20) with the aid of a Root catch but not before the tailender had helped Labuschagne add 51.
Labuschagne had made 70 when, just as happened with his second ball at Lord's, he was hit flush on the grille of his helmet by a steepling and rapid Jofra Archer delivery he could not evade in time.
But after being examined by the Australia team doctor, Labuschagne cleverly uppercut an 88 mph (141 kph) Archer bouncer for four when the World Cup-winner, who took 6-45 in the first innings, pitched wide of off stump.
Labuschagne was 74 not out when Pat Cummins's dismissal left Australia 226-8.
But rather than being denied a century in his seventh Test by a lack of partners, he ran himself out instead.
Labuschagne, who had demonstrated a degree of application beyond England's batsmen so far this match, ignored the old rule of 'never run on a misfield' when Joe Denly fumbled at third man and then failed to beat his throw to Bairstow.
But he could take pride in a 187-ball innings featuring eight fours.