First-innings centurion Usman Khawaja, who was on 35 not out, and all-rounder Cameron Green, who was unbeaten on 26, will resume at the Sydney Cricket Ground for final session with Australia 149 for four.
Australia had snuffed out England's first dig for 294 in the first hour of the day but they did not have it all their own way as they looked to build on the 122-run lead their 416-8 declared gave them.
Openers David Warner (3) and Marcus Harris (27) were removed before lunch and paceman Mark Wood struck in the first over after the break to dismiss Labuschagne (29) for the third time in succession.
All three batsmen were caught behind by England substitute fielder Ollie Pope, who was keeping wickets in place of the injured Jos Buttler and Jonny Bairstow.
Jack Leach, who had earlier deceived Harris with his spin, got his second wicket when a delivery skidded on to Smith's stumps when the former Australia captain was on 23.
Australia's batting has run deep all series, however, and Green and Khawaja, who scored 137 in the first innings, had put on 63 for the fifth wicket at tea.
Earlier, Scott Boland was again to the fore as Australia swiftly dispatched England's last three batsman for the addition of 36 runs to their overnight score.
Boland finally ended Bairstow's innings on 113 and finished off the England batting by having Stuart Broad caught behind for 15.
The 32-year-old quick took 6-7 on debut as England were skittled for 68 in their second innings in the third Test in Melbourne, giving Australia an innings and 14-run victory for an unassailable 3-0 lead in the five-match series. Boland finished with figures of 4-36, giving him 11 wickets at an average of 8.27 after his first three innings of Test cricket.