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.
A second bouncer by the bowler softened up debutant Rahane (7), who got hit on the helmet and didn`t recover from the psychological blow. Lyon took advantage of the situation as he got one to pitch on the rough as Rahane presented a tame catch to the backward short-leg fielder.
Operating from the Delhi Gate End, Lyon used the deteriorating pitch conditions to good effect, using the rough created outside the leg-stump well. Also he got awkward bounce that created problems for the Indian batsmen who time and again got beaten while trying to play for the turn.
Even Tendulkar (32) found it difficult to hit him. Having survived a confident leg before appeal in the post-lunch session, the veteran did hit five boundaries with three lovely ones of Siddle. But the offie pushed one quicker through the air and it hurried off the surface to find the batsman plumb in-front.
Skipper Mahendra Singh Dhoni hit a few boundaries en route to his 24 but he committed early into a slow bouncer from Pattinson to give a simple catch to mid-wicket.
Earlier, the makeshift opening stand of Pujara and Vijay turned out to be a productive one as it yielded 108 runs in 25 overs with both players helping themselves to contrasting half-centuries.
While Pujara`s 76-ball 52, with five boundaries, was a busy innings, Vijay, who has been in fine form since the Hyderabad Test match, contributed a useful 57 off 123 balls and hit eight fours.
However, the Tamil Nadu opener was subdued after the completion of his 50 as his next seven runs came off 38 deliveries.
At the onset, Pujara played a majestic backfoot cover drive off Pattinson after Vijay opened his account with a streaky boundary past the slip cordon.
Pattinson drifted one onto his pads and he promptly got his second boundary. Then came the best shot of the morning session as he hit left-arm pacer Mitchell Johnson for a straight drive.
The three boundaries gave Pujara confidence to get off the blocks. Pujara's stroke-making must have inspired Vijay as he elegantly played pacer Pattinson through the wide mid-on area.
The first five overs of the innings produced 34 runs and it looked as if Vijay and Pujara were already in the Indian Premier League mode, which is scheduled to start in 10 days' time from now.
The 50-run partnership was completed in the 10th over. Pujara was finally dismissed after completing a well deserved half-century. Facing a Lyon delivery, Pujara played for the turn, but the ball went straight to hit the off-stump. Pujara faced 76 balls and hit five boundaries in the process.
Kohli also didn't stay long as Lyon trapped him plumb-in-front for one.
Around 1:25 pm, Tendulkar walked out amid standing ovation from the 20,000 odd weekend crowd, and got off the mark off the 10th delivery that he faced.
In the morning, Australia finished their first innings on 262, adding 31 runs to their overnight total of 231 for eight.
Siddle completed his maiden Test fifty but was done in by a straighter one from Ashwin who completed his fourth five-wicket haul in the series. Siddle scored 51 off 136 balls with four boundaries. Ashwin finished with figures of five for 57 in 34 overs.
The Australian innings lasted a shade over 14 overs as Pattinson's (30) dogged resistance ended with Pragyan Ojha getting his 100th Test wicket. Ojha completed the feat in his 22nd Test and is the third fastest to reach the milestone after Erapalli Prasanna and Anil Kumble.