India won the toss and chose to bowl first in the two-day tour match at Manuka Oval, one of two warm-up matches they will play in the Australian capital before the first of four Tests starts on December 26 at the Melbourne Cricket Ground.
The tourists had said they wanted to use the match to give their relatively inexperienced bowlers plenty of practise in Australian conditions.
Opener Wes Robinson smashed 143 but South Australia's Tom Cooper, who has played for the Netherlands in one day internationals, bettered that with a brutal unbeaten 182 off 194 balls with 24 fours and three sixes. The pair shared a partnership of 226.
Right-arm paceman Umesh Yadav, who impressed in his first Test series against West Indies last month, was the pick of the Indian bowlers, taking three wickets at a cost of 39 runs.
Left-arm spinner Pragyan Ojha was the most costly, taking two wickets for 149 to do his personal tussle with off-spinner Ravichandran Ashwin for a Test spot no good.
The Chairman's XI declared when Dean Solway was caught behind off the medium pace of Ranganath Vinay Kumar for five after 86 overs to bring up stumps.
The India side, which boasts a strong batting line-up featuring Rahul Dravid, Sachin Tendulkar and VVS Laxman, will have the same number of overs, requiring 399 for victory on Friday.
Sharma bowled the first over but made a couple of trips off the pitch before departing for good midway through his sixth. A team spokesman said he had not suffered an injury.
India, who have never won a test series in Australia, play a three day match against a more experienced Chairman's XI on the same pitch starting next Monday.
Reuters