But the most difficult part of the ascent is yet to come as the tourists battle to salvage a draw which would keep alive the Border-Gavaskar Trophy series in which they trail 0-1.
That they were able to bat with some security on the third day -- to be 4-338 at the close -- was due largely to Matthew Hayden (83) and Simon Katich (64).
Their first significant opening stand of the series provided a solid platform for the middle order batsmen.
And their efforts were not wasted.
Captain Ricky Ponting (87) Mike Hussey (53) and Michael Clarke (21no) ensured at the very least that Australia's defence of their crown will make it to the fifth day at the Feroz Shah Kotla Ground.
Hussey's late dismissal, bowled by a peach of a ball from Virender Sehwag (3-62) that broke past his groping blade to pluck off stump, demonstrated the enormity of the struggle ahead.
Though only four wickets fell on the day, there was an ever-present sense of danger, as the home attack once again outdid their visiting counterparts in terms of swing, spin, accuracy and inventiveness on a pitch that will be quite a riddle to bat on by the end of the match.
"You want all of your batsmen to make hundreds and that didn't happen today and it's got to happen tomorrow," Hayden said of the failure of any of the half centurions to go further.
"I think the longer we actually put time in at the crease tomorrow the more it's going to damage India. " India played for the most part without captain Anil Kumble, who was taken to hospital for stitches to a deep cut on his left hand, sustained when he made a flying but fruitless dive to intercept an airborne Hayden drive.
Sehwag and Amit Mishra (1-95) wheeled away deviously for the hosts, while Ishant Sharma (0-46) and Zaheer Khan (0-57) curled the old ball usefully in the afternoon.
"Sehwag bowled exceptionally well," Hayden said.
"He used the conditions as good as any other bowler today, he had variation, he had spin -- some of the balls he was bowling, if Mahendra Dhoni didn't have a helmet on they would've hit him in the face. " Resuming at 0-50, Hayden was struck on the helmet by the first ball of the day from Zaheer.
However ,there were plenty of runs to be had on a still decent pitch and fast outfield, and both batsmen eventually were able to open their shoulders, raising a century stand in 125 minutes and 175 balls.
Katich was more fluent for the most part, but Hayden struck the ball cleanly in his first score of any note on this tour, and deposited one lusty pull shot beyond midwicket for six off the bowling of Mishra.
Lunch hoved into view, but Katich was unable to reach it, beaten in flight by Mishra and bowled by a leg break that snapped back sharply out of the rough.
Hayden battled on in the afternoon, keeping the runs ticking over with his usual combination of muscle and grit.
Sehwag was eventually rewarded for his persistence when Hayden went fatally back to a delivery that did not turn and was adjudged lbw by umpire Billy Bowden.
Like Hayden, Ponting seldom looked entirely comfortable against a diligent attack that once again extracted more from the pitch and the air than the Australians could manage.
His boundaries were frequent but came as much from nicks as full blooded strokes, and Sharma again gave him several frights.
Nonetheless, Ponting seemed to have weathered the storm, and it was a surprise when he charged contemptuously at Sehwag and was bowled when the ball spun neatly back between his swinging bat and advancing pad.
Clarke found batting a struggle for much of his stay, pushing uncertainly at Mishra's dipping legspin when he wasn't being struck on the gloves by a prancing Sehwag off break.
Yet, unlike Hussey, he survived.
