At the Adelaide Oval, Lyon took 5-134 as the visitors lost five wickets for just 75 runs in this morning session and surrendered a lead of 73 runs to the hosts.
Australia had declared their first innings at 517/7 on day three yesterday.
The off-spinner became only the second spinner in 46 years to take five wickets in a Test innings at home against India, following Bob Simpson who scalped 5-59 at Sydney back in 1967-68. He was ably supported by Peter Siddle (2-88) who recovered from a stomach bug.
After a quick change-around then, David Warner (13*) and Chris Rogers (19*) came out to bat for a second time in this match. Mohammad Shami (0-7) and Ishant Sharma (0-10) were the opening bowlers for India. Spin was introduced in only the sixth over as Karn Sharma (0-8) was brought on to make use of the rough patches.
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Another sign of the deteriorating pitch was when Murali Vijay (0-7) too was brought on, with Varun Aaron kept away from the attack before lunch. At the break, Australia were placed at 32/0 in 10 overs, a total lead of 105 runs.
They had managed to put on 32 runs for the sixth wicket, with Rohit looking to attack Lyon when the spinner was introduced into the attack. It didn't work as after getting a boundary in the 108th over, the batsman tried to turn one away for a single but only ended up offering a return catch. Lyon snapped it up, diving to his right, and then went on to wreak more havoc six overs later. Rohit scored 43 runs off 89 balls, hitting 5 fours.