Australia lost 5-30 in a horror 21-over period in the middle session to go from being in a solid position at 2-106 to 7-136 and in real danger of being bowled out for an embarrassing first innings score.
However, a fighting 46 from Smith, and now an unbeaten 47 from Siddle and 11 from Pattinson has seen Australia safely reach 8-231 at stumps on the first day.
Ravi Ashwin has 4-40 for India with Ravindra Jadeja picking up 2-34 and Ishant Sharma 2-35.
Australia made a solid start in the first session to be 2-94 at lunch despite losing David Warner for a duck and Phil Hughes for 45, but the middle session proved disastrous.
Spinners Ashwin and Jadeja combined to take all five of those wickets between them to now leave Australia in trouble at 7-153 at tea with Smith not out on 25 and Siddle on five.
Australia lost 5-30 in just 21 overs before Smith and Siddle came together at the crease.
Australia came into the final Test of the disastrous series against India making five changes to the side with Shane Watson replacing Michael Clarke as captain.
Matthew Wade took Brad Haddin's spot with the gloves, Glenn Maxwell took over as the all-rounder from Moises Henriques, Johnson gained Mitchell Starc's spot as the left-arm paceman and James Pattinson returned in favour of Xavier Doherty.
Watson won the toss for the visitors and elected to bat first and it was a disastrous start for Australia when Warner played a loose shot outside his off stump to Ishant Sharma, and only managed to edge it to Virat Kohli in the slip.
He fell without scoring and Australia was 1-4 in the second over, but Hughes enjoyed his chance to start his innings against the quick bowlers and he and Cowan took the score to 71 before Hughes was bowled by Sharma for 45. He hit 10 boundaries in that knock.
Cowan and Watson then survived until lunch, with Watson just getting away with a tight stumping call, but after the interval things all started to go awry for Australia when Cowan was bowled around his legs by Ashwin for 38.
Australia was then 3-106 and 4-115 when Watson was stumped for 17 by MS Dhoni off Jadeja. Wade then made just two before being caught by Murali Vijay off Ashwin, and Maxwell hit a four and six quickly, but was gone for 10 soon after to leave Australia in desperate trouble at 6-129.
Johnson then made just three from 22 balls before being bowled by Ashwin.
However, Siddle then showed good defensive abilities to hang in there with Smith until tea, and then after the break Smith started to be a little more expansive before falling for 46 from 145 balls with three fours and two sixes.
Siddle and Pattinson safely survived until stumps, though, to at least avoid embarrassment for Australia.
It will still take a remarkable effort from here for Australia to avoid a four-nil clean sweep in the series even though it's only the first day in Delhi.