Hussey hit a half-century to take Australia over the 450-run mark.
Clarke hit his maiden double century to take the Australian lead over the 200-run mark.
Clarke is the 34th Australian to hit a double century in Test cricket.
Clarke was at 170 with Hussey for company as Australia took a 158-run lead at the end of the second session.
Ishant Sharma struck with the second new ball when he had Ricky Ponting caught by Sachin Tendulkar at point. Ponting added 288 runs with Clarke for the fourth wicket.
Ponting hit 14 fours in his 134-run knock before falling to Ishant.
The much-needed breakthrough came after captain Michael Clarke reached 150 as he and Ponting took Australia over the 300-run mark.
Ponting scored a century almost after two years as his last ton (209) came against Pakistan in Hobart in January 2010. Ponting cracked his 40th ton in 150 balls with the help of 11 boundaries.
The two experienced Australian batsmen stitched an unbeaten 200 runs stand for the fourth wicket and put on the backfoot in the game.
Michael Clarke slammed his 18th Test century to take Australia into commanding position at lunch on the second day.
At lunch on a steamy day at the Sydney Cricket Ground, Australia were 236 for three with a vital 45 runs lead.
Clarke's fourth Test century against India came off a glorious cover drive off Ishant Sharma in the last over before lunch. It was Clarke's second Test century of the Australian summer season after scoring 139 against New Zealand in Brisbane last month.
India bowlers toiled hard in the first session as they conceded 120 runs in 27 overs without taking a single wicket.
Ponting continued his good run as he scored yet another fifty which brought up in style with a classy square cut played slightly on the front foot to the boundary. Ponting also became the third player in Test history to get 100th score in excess of 50.
Former skipper 61st Test fifty and 12th against India came in 74 balls that included six boundaries. This was his 6th half-century in a row against India.
Clarke raced to his fifty on the second delivery of the day when he flicked it through mid-wicket to complete his 22nd Test half century and 6th against India. Clarke completed his quick-fire fifty in just 60 balls with the help of seven boundaries.
Australia ended the first day well on top at 116/3 after restricting India for paltry 191, resumed their first innings on Day 2 of the second Test at the Sydney Cricket Ground.
Zaheer Khan started with a bang as he gave two quick blows before the Australian total reached double-digits, followed by one more in the 30s, raised Indian hopes, but the home team recovered well through a fine unbeaten partnership of 79 runs between Ricky Ponting and Clarke to end the first day at 116/3.
MS Dhoni's decision to bat first after winning the toss backfired badly as India's famed batting line-up came a cropper yet again against a disciplined Australian pace attack.
Young James Pattinson ripped the heart out of India's line-up, claiming four of the top-five batsmen while Peter Siddle and Ben Hilfenhaus claimed three wickets each.
Dhoni (57*) was the highest scorer of the Indian innings which also was his first half century in Australia. Sachin Tendulkar faltered again in his quest for a 100th international century as he chopped a widish Pattinson delivery onto his stumps for 41.
