But then, batting with the tail, Pujara accelerated and made his next 50 from 78 balls to score his 16th Test century.
India finished the day on a respectable 9-250 after it looked like they may have been skittled for a sub-par score.
However, Pujara held firm at the other end and stitched a solid stand with Ravichandran Ashwin for the seventh wicket.
Australian bowling coach David Saker confirmed it was a premeditated plan for Hazlewood, Cummins and Mitchell Starc to pitch it up and lure India's batsmen into false shots.
Day 1 Report: "Australia's fifth bowler has been India's shot selection", said Mark Butcher on commentary, and the former English Test batsman wasn't wrong.
"It was hot but I was set and I knew I could play my shots".
"It's not an easy wicket to bat on", he said. The offspinner took the only two wickets in the middle session but could not take wickets after tea.
"I would have liked to have actually seen Tim Paine bat at No.6 and Mitch Marsh at No.7 to give him a bit more freedom down the order and also that all-rounding option".
Starc hoped to be more consistent with the ball in the coming days.
Openers K L Rahul and Murali Vijay fell cheaply losing their wickets after being caught off by Finch in Hazlewood's spell and Starc respectively.
It took a screamer of a catch by Usman Khawaja at gully off the bowling of Pat Cummins to dismiss superstar Kohli for three. His run out, the result of a brilliant direct hit by Cummins at the non-striker's end, prompted the umpires to end the day's proceedings.
Khawaja dived and snared the ball in his left hand.
The dismissal of Kohli, who has scored five centuries in his two previous Test tours of Australia and rates Adelaide his favourite overseas ground, sparked wild celebrations.
Ajinkya Rahane (13) was caught by Peter Handscomb off Josh Hazelwood.
India captain Virat Kohli opted to bat first but their top order crumbled against Australia's attack, with numerous batsman guilty of poor shot selection.
A crowd of 23,802 braved the heat but the figure was considerably less than opening days for the Adelaide day-night tests of the past three years.
India have never won a Test series in Australia and their recent oversees record has also been poor with 1-2 loss to South Africa in February and 1-4 defeat to England in September.