The Australian made a century as Glamorgan sought to chase down a victory target of 593, a world record chase.
The match against Gloucestershire - rivals from across the River Severn that divides England and Wales, in which Glamorgan lies - came down to the last delivery after four days play.
Glamorgan had reached 9-592, leaving last man Jamie McIlroy requiring a single off the final ball of the match to achieve the win.
Gloucestershire wicketkeeper James Bracey, standing back - but not as deep as usual, took off his right glove in case the batters ran a bye and he needed to shy at the stumps.
Ajeet Singh Dale bowled, McIlroy swung and edged, and Bracey took a stunning right-hand catch to spark scenes of mayhem at Cheltenham.
WOW— Vitality County Championship (@CountyChamp) July 3, 2024One ball left, one run to win and set a new world record.James Bracey is not wearing a glove on his right hand.And he takes this catch. pic.twitter.com/4oR4AsjE9H
Bracey, who briefly played for England, had been wearing pads for more than 225 overs having batted the last 74 of Gloucestershire's second innings when making an unbeaten double century.
Sam Northeast (187) and Labuschagne (119) led Glamorgan's attempt to eclipse the highest run chase of all time, the 536 successfully pursued by West Zone in a Duleep Trophy match against South Zone in India in February 2010.
They failed in that quest but do go into the record books with the highest fourth-innings score in any first-class match played in England and the third best of all time.
In the first innings Gloucestershire had been bowled out for 179 and Glamorgan 197. The home side then scored 5-610, which at the time seemed more than enough.
The result left both sides mid-table in the second division.
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