Australia 263 and 61 for 1 lead India 262 (Axar 74, Lyon 5-67) by 62 runs
India's formidable lower order, led by Axar Patel, again played a crucial role after Nathan Lyon had taken five wickets to turn what looked like being a significant deficit on a tricky Delhi pitch into a one-innings shootout of a Test with Australia holding the advantage of bowling last.
The home side had slipped to 139 for 7, with Lyon doing the majority of the damage in the first two sessions, as Australia's opening-day 263 took on imposing proportions. But Axar and R Ashwin then added 114 for the eighth wicket to leave the difference just one run.
Australia had extended that briskly to 62 by the close. Travis Head, opening in place of the subbed-out David Warner, made a very punchy start although they lost Usman Khawaja to a brilliant catch at leg slip from a paddle-sweep. However, Marnus Labuschagne signalled his, and Australia's intent, by taking three fours in an over off Ravindra Jadeja.
The game would likely have already gone from India, though, if it wasn't for Axar. He produced a magnificent innings during which some of his off-side strokeplay was the highlight, particularly a flat cover-drive six against Todd Murphy, and it needed a reflex catch at mid-on from Pat Cummins to end things when he was looking to cut loose following the departure of R Ashwin.
Ashwin had enjoyed milking his promotion to No. 3 as nightwatchman in Nagpur, but neither he nor Axar would look out of place higher up the order. Ashwin took the role of senior player seriously, constantly encouraging Axar although he did not appear to be having many concerns as he backed up the 84 he made in the first Test.
Things had looked much different for the first half of the day. Rohit Sharma and KL Rahul had formed a solid opening stand, but once Australia got their first inroad the game took on another complexion.
Lyon made the opening incision when he trapped the under-pressure Rahul with one which straightened from around the wicket. He then produced a brilliant piece of bowling to defeat Rohit with a delivery that skidded on into the stumps.
Cheteshwar Pujara had been cheered to the crease in his 100th Test but was unsettled throughout a brief stay before he was trapped lbw for a duck by Lyon with a brave DRS call, instigated by Alex Carey, after Australia had burned their first two reviews very early with poor, speculative requests. They had used them all by the 25th over.
This time the replays showed that the ball had brushed Pujara's front pad first, it was smashing halfway up middle and India were 54 for 3.
It got better for Australia soon after when Peter Handscomb did remarkably well to keep his composure at short leg and hold a catch as it rebounded off his body from a strong flick by Shreyas Iyer. After a somewhat difficult first Test, albeit where fortune did not favour him, Lyon had four.
India then steadied across the next 20 overs as Virat Kohli, looking very secure and judging length brilliantly, formed a solid alliance with Jadeja who played cautiously until he fell lbw to Murphy which led to another flurry wickets.
A key moment came when Matt Kuhnemann claimed his maiden Test wicket by gaining a borderline lbw against Kohli. The decision, as Kohli played forward with bat and pad together, was given out on field. Kohli reviewed and it could have been viewed that impact with bat and pad was simultaneous.
However, third umpire Richard Illingworth ruled it was pad first - not having conclusive evidence to go against the on-field call - and it was just clipping leg stump. As Kohli watched replays in the dressing room he was still coming to terms with it.
It was a memorable scalp for Kuhnemann, who only arrived in India a week ago, and overall it was a commendable debut outing from the left-arm spinner.
When Lyon had KS Bharat caught at slip off a gloved sweep to complete his five-wicket haul, a three-figure - and likely match-deciding lead - was within reach for Australia. But India's batting was far from finished.
Shortly before tea, Axar took on Kuhnemann, sending consecutive balls for four and six to lay down a marker, but it was the assuredness of the defence as much as the attacking strokes that stood out. However, he could have been caught at slip on 28 off Lyon had Steven Smith been able to stay low on his stance and another tough chance scooted past Matt Renshaw at leg slip from Ashwin.
Axar brought up his fifty by mowing Kuhnemann over deep midwicket for six and crunching back-to-back boundaries against Cummins registered the century stand.
It was becoming a little desperate for Australia but the new ball finally wrapped up the innings, although probably not entirely by design. Ashwin clipped a leg-stump half-volley to square leg where Renshaw plucked it out of the air and Axar could barely believe Cummins was able to cling onto his well-struck drive at mid-on. After two innings, the teams could not be split, but Australia made the early moves in the decisive second half.