India finished the day on a respectable 9-250 after it looked like they may have been skittled for a sub-par score.
Pujara put on vital partnerships with R Ashwin and Ishant Sharma in the end, as the Australian pacers exhausted.
Cummins provided the breakthrough of Ashwin just before the new ball. "I knew I had to stay patient and wait for the loose balls".
"Lyon understands the pace of the wicket, the bounce that it's going to provide him, and where the fielders should be, " Kohli said.
Pujara said he would now turn to coaching India's bowlers on the best methods for extracting the most from the Adelaide pitch.
Australia's early aggressiveness was blunted by the heat with the temperature hitting 39 degrees Celsius (102 degrees Fahrenheit) during the final session, forcing Australia captain Tim Paine to juggle his pacemen with sharp bursts.
Paceman Mitchell Starc was one of four Australian bowlers to claim two wickets and said his team was in an excellent position. The offspinner took the only two wickets in the middle session but could not take wickets after tea.
"I was a bit disappointed but I had to take that single because only the last two balls were left and I thought I should be on strike, so I took the chance but he fielded brilliantly", he explained.
"For the most part we were exceptional with the ball today", said Starc.
The dismissal of the prolific skipper, who rates Adelaide as his favourite overseas ground, sparked wild celebrations. Rahane, who was dropped by debutant Marcus Harris at short-leg off Lyon, chased a wide delivery from Hazlewood into Peter Handscomb's hands at second slip.
"So I don't think spin bowling is a big threat, but it seems to me that Australia are anxious about the spinning options of India, deciding to go with Handscomb who's such a good player of spin".
In day-night Tests in the past three years, Adelaide's opening-day crowds numbered around 47,000, 32,000 and 55,000.
It was nonetheless a positive finish for Virat Kohli's side who had slumped to 86 for five after lunch, falling to a combination of awful shot-making and fierce Australian pace after winning the toss.