Vijay and Rahul produced a 50-run partnership for the first time outside of India. Starc returned into the attack after the drinks break and broke the stand by dismissing Vijay, who edged to second slip.
India had a first-innings lead of 15 runs after bowling out Australia for 235. After sweltering conditions during the opening two days, only 10.4 overs were bowled in the first session.
Travis Head top-scored for Australia with 72 and equalled his highest test score. He received invaluable support from Lyon, who hit an unbeaten 24 from 28 balls.
India's four-pronged attack shared the wickets with paceman Jasprit Bumrah and spinner Ravi Ashwin picking up three apiece.
Australia resumed at 191-7 with Head on 61 not out and Starc unbeaten on eight.
Twenty minutes into the session, under the lights, Starc recklessly drove a full Bumrah delivery and edged to be caught behind.
Play was then interrupted for an hour due to rain.
Lyon dominated the strike in his partnership with Head and counterattacked with a six off a hook shot from Mohammed Shami's first delivery.
Two balls later, Head played away from his body to be caught behind and Hazlewood fell first ball, leaving Shami on a hat-trick when Australia bats in their second innings.
Twenty overs were eventually lost on day three after the rain delays.
- AP
