The 23-year-old had struggled with cramps after taking two wickets on the opening day, but overcame his fitness concerns to return figures of 5-68 as the tourists were bowled out for 408.
Hazlewood was pleased with the way he responded to the pain he had suffered on a stifling hot Wednesday at The Gabba.
"I'd never experienced cramps like that before," he said. "It was painful at the time, but I got through it and am happy with how I bowled today.
"I obviously started the summer well in the limited-overs format, but to do it in a Test match is something I'd always dreamed of.
"Obviously it gives me massive confidence. I felt I was bowling very well with the white ball, the ball felt like it was coming out the best it ever has, so now to put performance like that in a Test match is very good for the confidence."
The debutant also had praise for the rest of Australia's bowling attack, after India's last six wickets went down for 87 runs on Thursday.
"We started a bit hesitant," he added. "In patches on day one it was good, but we came out this morning and bowled beautifully.
"I think [we pushed our length] a bit fuller to make them play and we got a few nicks through.
"We all came out well and bowled to our plan and picked up the last six wickets for about where we wanted them."
The hosts subsequently closed on 221-4, trailing by 187, with new captain Steve Smith unbeaten on 65.