Ross Taylor, who put on 76 for the third wicket with Williamson and made 290 in his previous Test in Perth, was on 66 and BJ Watling was yet to score.
Smith’s freak catch was a key moment, as the Kiwis slumped to 97 for five by losing three wickets for just 20 runs.
Starc (4-31) did the damage with four wickets, including those of Henry Nicholls (7) and night watchman Neil Wagner (0) in successive balls.
However, Australia had also lost opening bowler Josh Hazlewood (1-0) with a left hamstring injury.
Hazlewood bowled opener Jeet Raval for a duck in his first over, but managed just two balls in his second before pulling up short during his run up.
He left the field immediately with a devastated demeanour, becoming the second fast bowler to succumb to injury in two days of scorching Perth heat.
Kiwi debutant Lockie Ferguson was forced out the game on the first day by a calf injury.
The wicket of Raval followed the dismissal of Tom Latham in the very first over, easily caught and bowled by Starc in his follow through.
Having claimed the two openers in quick time in favourable bowling conditions Australia looked in total control, but Williamson and Taylor rode their luck early and then settled in as the home side was forced to turn to former wicketkeeper Matthew Wade to send down a couple of overs of erratic medium pace.
Replays suggested Wade actually had Williamson caught behind on 13, but the Australians didn’t review even though Smith seemed confident it was out.
Earlier, Labuschagne’s 143 was the foundation of an Australian innings that lasted just a few balls shy of five full sessions as the mercury again climbed towards 40 degrees Celsius (104 Fahrenheit) and a bushfire broke out adjacent to the ground.
Labuschagne looked set for his third successive innings over 150 until he was bowled by the determined Neil Wagner (4-92).
The 25-year-old hadn’t given a chance in reaching 143, but walked a little far across his stumps and the ball crashed into his leg stump to reward Wagner for a spirited spell.