But Sachin Tendulkar (47) helped India towards safety before VVS Laxman (59no) and Sourav Ganguly finished the job.
Dinesh Karthik, Mahendra Dhoni and VVS Laxman were all dismissed cheaply for the second time in the game.
He had promoted VVS Laxman up the order and the batsman repaid the faith with a staggering match-winning 281.
Rahul Dravid was out shortly after for 74 but Sachin Tendulkar (53) and VVS Laxman (62) piled on further runs.
Coming in ahead of the midsummer arrival of VVS Laxman, Prince hit 497 County Championship runs in five matches at 62.12.
Tendulkar and VVS Laxman (42 not out) did the most to repel the Australians as 10 overs were lost to bad light.
The only flaw in his innings came on 60 when he edged a chance to VVS Laxman at first slip, which was dropped.
Among his victims was India skipper VVS Laxman, who hung around for almost three hours for 31 before being caught by Jean-Paul Duminy.
With Tendulkar, former captains Rahul Dravid and Sourav Ganguly, and VVS Laxman all in their mid-30s, there have been calls for the introduction of some younger talent.
The pair put on 129 for the second wicket to guide Lancashire to a strong position of 140-1 following the early loss of VVS Laxman.
Both sides made three changes, India recalling VVS Laxman, Ashish Nehra and Harbhajan Singh, while Bangladesh brought in Manjural Islam Rana, Tareq Aziz and Faisal Hossain.
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Karthik shared 129 in 41 overs with left-hander Gautam Gambhir who made 81, and skipper Rahul Dravid and VVS Laxman added a quickfire 75 in 19 overs.
Law, Horton, Luke Sutton and Glen Chapple all fell before lunch and tea and only VVS Laxman (53) looked like getting the big score the visitors wanted.
He was on 102 when Sharma had another slice of bad luck, an edge falling fractionally short of VVS Laxman at the second of the two wide slips.
Then Krejza turned the match with two wickets in two balls, firstly uprooting the leg-stump of VVS Laxman with a ball than spun from outside off via the inside edge.
Sreesanth revealed he had bowled to a plan to lure left-hander Strauss into playing at a wide ball and it worked to perfection when VVS Laxman took an sharp catch.
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The selection raises the prospect of India's "fab four" batsmen - the enormously experienced quartet of Ganguly, Sachin Tendulkar, Rahul Dravid and VVS Laxman - taking on a fledgling Australian bowling attack.
Returning from a six-week layoff because of an abdominal strain, Tremlett had VVS Laxman and Steve Croft caught by Pothas, Faf du Plessis snared by Benham and then trapped Kyle Hogg lbw.
An experimental Lancashire side, missing the likes of captain Glen Chapple, Mal Loye, VVS Laxman and Francois du Plessis, were skittled for just 166 in the 40th over after they batted first.
With three whole days of the match to come, and Sachin Tendulkar, VVS Laxman, Yuvraj Singh and Mahendra Dhoni yet to bat, India are on course for a truly eye-watering first innings score.
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The much-needed breakthrough came via a well-disguised slower ball from Sharma, when Haddin's forward prod spooned up into the air for the perfectly-placed VVS Laxman at short extra cover to leave the tourists 350-6.
When Dravid was caught behind off Morne Morkel that was the start of a mini-collapse, with VVS Laxman edging Lonwabo Tsotsobe to gully and Suresh Raina hopelessly fending Jacques Kallis to Paul Harris at slip.
Already without batsmen Rahul Dravid and Yuvraj Singh because of injuries, the hosts suffered a setback before the start of play when the experienced VVS Laxman failed to recover in time from a finger problem.
Matt Prior, who dropped Tendulkar on 20 on day one, perhaps tried too hard to atone for that error when VVS Laxman edged the luckless Ryan Sidebottom, who had beaten the bat on several occasions.
But the Essex man made just six more runs before edging Ishant Sharma tamely to VVS Laxman at second slip, which brought an out-of-form Bell in to partner Strauss, who made a duck in the first innings.
Tendulkar smashed 14 fours and a six during a 243-ball stint that, added to contributions of 109 by VVS Laxman and 67 from Sourav Ganguly, carried the tourists to 532 all out in response to Australia's first-innings score of 463.
Ganguly and Mohammad Kaif have not been picked for the opening one-dayers because of injury and fellow batsman VVS Laxman has been dropped, leaving room for Test opener Gautam Gambhir to try and prove himself in the shorter form of the game.
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