At stumps after an intriguing second day's play, India struggled their way to 266 for eight despite a century-plus opening stand between Cheteshwar Pujara (52) and Murali Vijay (57) after the visitors had scored 262 in their first innings.
The bulk of the damage was done in the post-tea session when India lost six wickets as the Australian bowlers looked menacing for the first time.
If India manage a lead of even 50 runs, it could turn out to be a decisive one considering Australia's lack of firepower to counter the Indian spinners.
Curator Venkat Sundaram designed the pitch at the Feroz Shah Kotla keeping in mind the requirements of the Indian team, but it boomeranged on the hosts instead, as Lyon (5/94) extracted sharp turn and bounce to get rid of top-order players like Sachin Tendulkar, Virat Kohli, Pujara and debutant Ajinkya Rahane.
Ravindra Jadeja survived a hostile spell from James Pattinson and faced constant sledging from the close-in fielders as he fought his way to a fighting 43 before getting a questionable leg before decision off Glenn Maxwell.
Pattinson and Peter Siddle also got certain deliveries to rear up awkwardly from the good length spot, which caused trouble for the batsmen.
Having gone into tea at a relatively comfortable 114 for two, the trouble started in the final session with an inspired spell of fast bowling from Siddle.
A nasty bouncer accounted for Vijay as he lobbed a simple catch to wicketkeeper Matthew Wade.
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