Australia had resumed on day five on a turning pitch at 9-232 and were bowled out for 241 - a lead of 49.
No.11 Lyon was caught at short leg for 11 after adding 66 in 85 minutes for the 10th wicket with debutant Moises Henriques, who was unbeaten on 81.
Indian offspinner Ravi Ashwin claimed 5-95 after his seven-wicket haul in Australia's first innings.
Spinners Harbhajan Singh (2-55) and Ravindra Jadeja (3-72) were the other wicket-takers with Jadeja getting the breakthrough in the ninth over of the final day.
The second Test of the four-match series starts in Hyderabad on Saturday.
Officials say the game will go ahead as planned despite twin bomb blasts in the city last week which killed 16 and injured 117 people.
- AAP