Labuschagne was Test cricket’s leading run-getter last year with 1,104 runs and is carrying on where he left off in 2019.
The Kiwis finally got him out when Labuschagne was caught and bowled by leg-spinner Todd Astle.
Skipper Tim Paine provided support for Labuschagne to reach his double century before he was bowled between his bat and pad by de Grandhomme for 35.
Paine faced 92 balls and shared in a 79-run stand with Labuschagne to take Australia beyond 400.
Wickets fell quickly just before tea with James Pattinson bowled by Neil Wagner for two, Pat Cummins caught off Astle’s bowling for eight and Mitchell Starc hitting a breezy 22 off 21 balls before he was bowled by Wagner, who finished with three for 66.
The hosts lost two wickets on the second morning of the Test.
Matthew Wade was out in the day’s first over, bowled off-stump while attempting to sweep off-spinner Will Somerville for no addition to his overnight score of 22.
Melbourne Test centurion Travis Head fell to Matt Henry, cutting too close to his body and snicking to wicketkeeper BJ Watling.
The Kiwi bowlers had strangled his scoring shots and his 10 runs came off 42 balls.
Henry was bowling despite fracturing his left thumb on Friday. He had the injury strapped and placed in a splint to continue on playing.
The Sydney Test is being played against the backdrop of one of Australia’s most devastating bushfire seasons with at least 20 people losing their lives in blazes raging across the country, including on the outskirts of Sydney.
Play will be suspended in the match at the umpire’s discretion, should smoke significantly affect air quality or visibility, but the sky above the ground has remained clear so far.